Right triangle trigonometry review (article) | Khan Academy (2024)

Review right triangle trigonometry and how to use it to solve problems.

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  • John Thommen

    8 years agoPosted 8 years ago. Direct link to John Thommen's post “This is not correct. The...”

    This is not correct. The path of the swing is an arc so at the point where it is parallel to the support pole it would closer to the ground than at the point of full swing which is 2.75 meters. To make this example correct the 2,75 meters needs to be applied to the point where the swing is parallel to the supporting pole.

    (0 votes)

    • Jay Mitchell

      8 years agoPosted 8 years ago. Direct link to Jay Mitchell's post “You are correct that it i...”

      Right triangle trigonometry review (article) | Khan Academy (4)

      Right triangle trigonometry review (article) | Khan Academy (5)

      Right triangle trigonometry review (article) | Khan Academy (6)

      You are correct that it is an arc. However, the key to the question is the phrase "in full swing". The swing will be closer than 2.75 meters at the bottom of the arc. That is an interesting point that I hadn't considered, but not what the question is asking.

      (211 votes)

  • pratigyarana29

    a year agoPosted a year ago. Direct link to pratigyarana29's post “This is really fun to do”

    This is really fun to do

    (40 votes)

    • Marcus Pedersen

      4 months agoPosted 4 months ago. Direct link to Marcus Pedersen's post “I agree with you :)”

      I agree with you :)

      (3 votes)

  • veroaghe

    4 years agoPosted 4 years ago. Direct link to veroaghe's post “Shouldn't we take in acco...”

    Shouldn't we take in account the height at which the MIB shoots its laser. I'm guessing it would be somewhere from his shoulder. Maybe the answer wouldn't differ that much but it might make it a little more challenging to figure out. You would even be able to calculate the height the agent is holding his gun at with stretched arms when you know the angle he's keeping his arms at, his arm length and the length from his shoulders to the ground.

    (13 votes)

    • AHsciencegirl

      4 years agoPosted 4 years ago. Direct link to AHsciencegirl's post “Good point, let's estimat...”

      Right triangle trigonometry review (article) | Khan Academy (13)

      Right triangle trigonometry review (article) | Khan Academy (14)

      Good point, let's estimate :D.

      Men In Black are generally rather tall so it is fair to estimate the man is about two meters tall. The average arm length of an adult human is ~25 inches which equates to about 0.6 meters. If we assume that the man holds his arms directly above his head (not technically realistic but a fair assumption) then we can estimate the height of the LASER to be about 2.5 meters. If we subtract 2.5 from 324 we get 321.5. Arctan(321.5/54) = 80.465.

      That deviates from the ground angle by only 0.09%, so it probably wouldn't affect how he aimed the laser.

      If we assume he shot from shoulder height with his arms straight out, then that would be arctan(322/53.5) = ~80.567 which deviates from the ground angle by only 0.04%.

      (45 votes)

  • Aditya Lagoo

    4 years agoPosted 4 years ago. Direct link to Aditya Lagoo's post “What is the value of sine...”

    What is the value of sine, cosine, and tangent?

    (4 votes)

    • Hecretary Bird

      4 years agoPosted 4 years ago. Direct link to Hecretary Bird's post “The Sine, Cosine, and Tan...”

      Right triangle trigonometry review (article) | Khan Academy (18)

      The Sine, Cosine, and Tangent are three different functions. They do not have a value outright, it would be like trying to ask what the value of f(x) = x + 1 is. The trig functions give outputs in terms of the ratios of two sides of a triangle when we feed them the input of an angle measure.
      Sine outputs the ratio of opposite to hypotenuse
      Cosine outputs the ratio of adjacent to hypotenuse
      Tangent outputs the ratio of opposite to adjacent

      (13 votes)

  • Nadia Richardson

    4 years agoPosted 4 years ago. Direct link to Nadia Richardson's post “I am so confused...I try ...”

    I am so confused...I try my best but I still don't get it . I need someone to Break it down further for me? I never not understand math but this one really has me stuck.Thank you.

    (7 votes)

    • #1

      a year agoPosted a year ago. Direct link to #1's post “You might not be taking t...”

      You might not be taking trig anymore, but there is SOHCAHTOA - Sine = Opposite * Hypotenuse. sine is when you are given the opposite side from the angle and the hypotenuse of the triangle. Cosine = Adjacent * Hypotenuse. cosine is when you are given the adjacent side of the angle and the hypotenuse of the triangle. Finally, Tangent = Opposite * Adjacent. This is when you are given the opposite and adjacent sides of the angle. A side could also have x as its value and you solve for x.

      (7 votes)

  • Trevor Amrhannah Davis

    4 years agoPosted 4 years ago. Direct link to Trevor Amrhannah Davis's post “My problem is that I do n...”

    My problem is that I do not know which one is adjacent and opposite you the one closest to the angle is adjacent but if it doesn't show the angle then how am I supposed to know which one.

    (5 votes)

    • David Severin

      4 years agoPosted 4 years ago. Direct link to David Severin's post “Either the problem will t...”

      Either the problem will tell you which angle is the reference angle or it will give two sides and you can choose which of the two acute angles you can use as the reference angle.

      (5 votes)

  • seonyeongs

    4 years agoPosted 4 years ago. Direct link to seonyeongs's post “when solving for an angle...”

    when solving for an angle why does cos have a -1 on top?

    (2 votes)

    • Hecretary Bird

      4 years agoPosted 4 years ago. Direct link to Hecretary Bird's post “Trig functions like cos^-...”

      Trig functions like cos^-1(x) are called inverse trig functions. THey are the inverse functions of the normal trig functions. Where cos(x) would take in an angle and output a ratio of side lengths, cos^-1(x) takes in the ratio of adjacent/hypotenuse and gives you an angle, which is why we use it when solving for unknown angles.
      Note that cos^-1(x), (cos(x))^-1, and cos(x^(-1)) give three completely separate results.

      (9 votes)

  • Raghunandan wable

    7 years agoPosted 7 years ago. Direct link to Raghunandan wable's post “in question 1.1 the given...”

    in question 1.1 the given answer is approx 5.44 my calculator is giving 0.91 as an answer even in degrees mode

    (0 votes)

    • mathslacker2016

      7 years agoPosted 7 years ago. Direct link to mathslacker2016's post “The whole trick to the qu...”

      Right triangle trigonometry review (article) | Khan Academy (31)

      The whole trick to the question is that zero radians is an answer, and if you look closely, you see that no other answer other than 0*pi/10 will get you there, if zero is a possible answer for n. But then since sin(u) must be 20x, then you must still find an answer for every negative pi and positive pi in addition to finding the answer that will get you to zero, which is one of the possible answers. (And remember "every possible solution" must be included, including zero). So you need to pick the two answers that would get you to zero radians, plus positive and minus every other pi. It's a brutal question because the zero radians thing is a hard thing to remember, amidst so many answers that have every answer, but just happen to exclude zero radians. Harsh.

      (13 votes)

  • egeegeg

    5 years agoPosted 5 years ago. Direct link to egeegeg's post “when working out the inve...”

    when working out the inverse trig, is the bigger number always on the bottom?

    (2 votes)

    • David Severin

      5 years agoPosted 5 years ago. Direct link to David Severin's post “For sine and cosine, yes ...”

      For sine and cosine, yes because the hypotenuse will always be the longest side, but for tangent, it does not have to be, either the opposite or the adjacent could be longer than the other.

      (7 votes)

  • 91097027

    6 years agoPosted 6 years ago. Direct link to 91097027's post “do i have to be specific”

    do i have to be specific

    (2 votes)

    • NightmareChild

      6 years agoPosted 6 years ago. Direct link to NightmareChild's post “I agree with Spandan. If...”

      I agree with Spandan. If you aren't specific, because math has so many different terms, it's usually impossible to figure out exactly what you mean- there can be multiple answers to a question using or leaving out seemingly nonimportant words!

      (6 votes)

Right triangle trigonometry review (article) | Khan Academy (2024)

FAQs

How do you find the answer to a right triangle? ›

The Pythagorean Theorem gives us a2 + b2 = c2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b2 = 142 – 52 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

What are the trigonometric ratios of a right triangle? ›

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

How do you find the answer to a special right triangle? ›

To solve a 30° 60° 90° special right triangle, follow these steps:
  1. Find the length of the shorter leg. We'll call this x .
  2. The longer leg will be equal to x√3 .
  3. Its hypotenuse will be equal to 2x .
  4. The area is A = x²√3/2 .
  5. Lastly, the perimeter is P = x(3 + √3) .
Jul 7, 2024

What is a 45 45 90 special right triangle Khan Academy? ›

A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long. Created by Sal Khan.

Does 3/4/5 make a right triangle? ›

The 3-4-5 triangle rule states when the ratio 3:4:5 is present as the side lengths of a triangle, the triangle is a right triangle. The 3-4-5 triangle satisfies the Pythagorean Theorem which states that the sum of the squares of the two smaller sides in a right triangle equals the square of the longest side.

What is the formula for right triangles trigonometry? ›

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a2 + b2 = c2. Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

What are the 3 trig functions of right triangles? ›

Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side.

How do you find the formula of a right triangle? ›

FAQs on Right Triangle Formulas

These formulas are given as: Pythagoras Theorem - Formula: (Hypotenuse)2 = (Perpendicular)2 + (Base) Area of a right triangle formula: Area = 1/2 × Base × Height. Perimeter of a right triangle formula = Sum of lengths of 3 sides.

What is Soh Cah Toa? ›

SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function. SOH = Sine is Opposite over Hypotenuse. CAH = Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.

What is the formula for a right triangle? ›

FAQs on Right Triangle Formulas

These formulas are given as: Pythagoras Theorem - Formula: (Hypotenuse)2 = (Perpendicular)2 + (Base) Area of a right triangle formula: Area = 1/2 × Base × Height. Perimeter of a right triangle formula = Sum of lengths of 3 sides.

How do you find the missing number in a right triangle? ›

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2 a 2 + b 2 = c 2 , which is known as the Pythagorean Theorem.

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