Unit 5 Review

Pythagorean Theorem

100

What is the Pythagorean Theorem?

a²+b²=c²

200

What side of the triangle always has to be c?

Hypotenuse

300

Solve for x: x²+4²=5²

x=3

400

Solve for x: 

14.3²+23.2²=x²

x=27.3

500

A ladder leans against a wall. The base is 6 ft from the wall and the ladder is 10 ft long. How high up the wall does the ladder reach?

8 ft

Special Right Triangles

100

What are the 2 types of special right triangles?

45-45-90 and 30-60-90

200

Give the rules for a 45-45-90 triangle. Ex: leg= ?, leg=?, hypotenuse=?

x, x, x√ 2

300

Give the rules for a 30-60-90 triangle. Ex: leg= ?, leg=?, hypotenuse=?

x, x√ 3, 2x

400

If a 30-60-90 triangle has a short leg with a value of 8, what is the length of the long leg and the hypotenuse?

8√3 and 16

500

If the hypotenuse of a 45-45-90 triangle is 20, what are the lengths of the legs?

x=10√2

Trig

100

Name the 3 trigonometric functions we've talked about.

Sine, Cosine, and Tangent

200

What is the acronym we use to help us remember trig?

SOH-CAH-TOA

300

What trig function would you use if you are given the adjacent and the hypotenuse?

Cosine

400

A right triangle with angle of 34 degrees has a hypotenuse of 13. If you need to find the adjacent, how would you set up this equation?

cos(34)=x/13

500

A triangle with angle 26 degrees has an opposite side of 6. Find the hypotenuse.

13.7

Inverse Trig

100

When would you use inverse trig?

When solving for an angle.

200

How do you enter inverse trig on the calculator?

Trig button, bottom row, enter in the fraction.

300

Solve for the angle given: sin^-1=19/24

52.3

400

If you need to solve for an angle of a triangle are given the opposite and the adjacent, what trig function would you use?

inverse tangent -> tan^-1

500

A right triangle has an opposite side of 7 and an adjacent side of 11. Find the measure of the angle.

32.5 degrees

Angles of Elevation/Depression

100

What type of angle is formed when you look up at an object above you?

Angle of elevation

200

What type of angle is formed when you look down at an object below you?

Angle of Depression

300

The angle of depression is _________ to the angle of elevation.

Congruent

400

A person stands 20 ft from the base of a building. The angle of elevation to the top is 41°. How tall is the building?

17.4 ft

500

A drone is hovering above the ground and spots a person at an angle of depression of 38°. If the drone is 55 feet high in the air, what is the direct distance from the drone to the person (hypotenuse)?

89.3 ft