Geometry Review Right Triangles

PYTHAGOREAN THEOREM

100

What is the formula for the Pythagorean Theorem?

a2+b2=c2

200

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

10

300

A right triangle has a hypotenuse of 25 and one leg of 7. Find the other leg.

24

400

True or false: The Pythagorean Theorem works for all triangles.

False — only right triangles.

500

A ladder reaches 15 ft up a wall and the base is 9 ft away. How long is the ladder?

17.5 ft

SIMPLIFYING RADICALS

100

Simplify √50 .

5√2

200

Simplify √72

6√2

300

Simplify √18x²

3x√2

400

Write √75 in simplest radical form.

5√3

500

Rationalize the denominator: 6/√3.

2√3

SPECIAL RIGHT TRIANGLES

100

In a 45‑45‑90 triangle, if a leg is 5, what is the hypotenuse?

5√2

200

In 45-45-90, If the hypotenuse is 8√2, what is each leg?

8

300

In a 30‑60‑90 triangle, if the short leg is 7, what is the hypotenuse?

14

400

In 30-60-90 Triangle, If the hypotenuse is 20, what is the short leg?

10

500

in 30-60-90, If the long leg is 9√3, what is the short leg?

9

TRIGONOMETRIC RATIOS

100

Define sine.

Opposite ÷ Hypotenuse

200

Define tangent.

Opposite ÷ Adjacent

300

In a right triangle, sin⁡(θ)=3/5. Which side is the hypotenuse?

5

400

A triangle has opposite = 12 and adjacent = 5. What is tan⁡(θ)

12/5

500

A triangle has hypotenuse 10 and opposite 6. Find cos⁡(θ).

8/10 = 4/5

SOLVING WITH TRIG & INVERSES

100

Use sin⁡(30∘) to find the opposite side if the hypotenuse is 12.

6

200

Solve for x: cos⁡(60∘)=x/15.

x=7.5

300

Find the angle: θ=sin⁡−1(4/9).

26.4

400

A right triangle has opposite = 9 and adjacent = 14. Find θ.

θ=tan⁡−1(9/14)≈32.7∘

500

A ramp rises 3 ft over a horizontal distance of 12 ft. What is the angle of elevation?

θ=tan⁡−1(3/12) = 14 degrees