Perfect1600

Digital SAT · Solve it in Desmos

How to Solve Right Triangles and the Pythagorean Theorem on Desmos (Digital SAT)

Desmos takes the squares and the root cleanly, sparing you the arithmetic. Naming the hypotenuse and matching corresponding sides in a similarity are the calls it leaves to you.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for right triangles and the pythagorean theorem

The Desmos steps

  1. 1

    Type the theorem

    Enter sqrt(9^2 + 12^2) for a hypotenuse, and read the value.

  2. 2

    Solve for a leg

    Type sqrt(c^2 - a^2) with the known hypotenuse and leg.

  3. 3

    Compute a proportion

    For similar triangles, type the cross-multiplied ratio and read the missing side.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
13
B
14
C
15
D
17

A: Correct. c=52+122=169=13c = \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13.

B: Incorrect. This does not satisfy the Pythagorean theorem.

C: Incorrect. This does not satisfy 52+122=c25^{2} + 12^{2} = c^{2}.

D: Incorrect. This adds the legs instead of squaring them.

Explanation

c=25+144=169=13c = \sqrt{25 + 144} = \sqrt{169} = 13.

Easy example
A right triangle has legs of length 9 and 12 and a hypotenuse of length cc. Which equation correctly relates the side lengths?
A
9+12=c9 + 12 = c
92+122=c29^{2} + 12^{2} = c^{2}
C
92−122=c29^{2} - 12^{2} = c^{2}
D
9+12=c\sqrt{9} + \sqrt{12} = c

A: Incorrect. The legs are not simply added to give the hypotenuse.

B: Correct. The Pythagorean theorem states a2+b2=c2a^{2} + b^{2} = c^{2} for the legs and hypotenuse.

C: Incorrect. The legs are added, not subtracted, under the Pythagorean theorem.

D: Incorrect. The square roots of the legs are not summed to give the hypotenuse.

Explanation

For a right triangle, 92+122=c29^{2} + 12^{2} = c^{2}.

Medium example
A right triangle has a hypotenuse of length 25 and one leg of length 7. What is the length of the other leg?
A
14
B
18
C
20
24

A: Incorrect. This does not satisfy 72+b2=2527^{2} + b^{2} = 25^{2}.

B: Incorrect. This subtracts the lengths directly instead of squaring.

C: Incorrect. This does not satisfy the Pythagorean theorem.

D: Correct. b=252−72=576=24b = \sqrt{25^{2} - 7^{2}} = \sqrt{576} = 24.

Explanation

b=625−49=576=24b = \sqrt{625 - 49} = \sqrt{576} = 24.

Try it with the calculator

Question 1easy

A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

Question 2easy

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

Start the free diagnostic

Desmos questions

Can Desmos solve right triangles and the pythagorean theorem questions on the SAT?

Desmos takes the squares and the root cleanly, sparing you the arithmetic. Naming the hypotenuse and matching corresponding sides in a similarity are the calls it leaves to you.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master right triangles and the pythagorean theorem, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

See the full methodTake the free diagnostic