# Lesson 5

Working with Ratios in Right Triangles

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

A triangle has sides with lengths 8, 15, and 17.

1. Verify this is a Pythagorean triple.
2. Approximate the acute angles in this triangle.

### Problem 2

Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. How high is the kite?

### Problem 3

Triangle $$ABC$$ has a right angle at $$C$$. Select all measurements which would mean it has a hypotenuse with a length of 10 units.

A:

Angle $A$ is 20 degrees, $BC$ is 2 units

B:

$AC$ is 7 units, $BC$ is 3 units

C:

Angle $B$ is 50 degrees, $BC$ is 4 units

D:

Angle $A$ is 30 degrees, $BC$ is 5 units

E:

$AC$ is 8 units, $BC$ is 6 units

### Problem 4

What is a reasonable approximation for angle $$B$$ if the ratio of the adjacent leg divided by the hypotenuse is 0.45?

A:

27 degrees

B:

30 degrees

C:

60 degrees

D:

63 degrees

(From Geometry, Unit 4, Lesson 4.)

### Problem 5

Estimate the values to complete the table.

angle adjacent leg $$\div$$ hypotenuse opposite leg $$\div$$ hypotenuse opposite leg $$\div$$ adjacent leg
$$A$$ 0.31 0.95 3.1
$$C$$
(From Geometry, Unit 4, Lesson 4.)

### Problem 6

What is the length of side $$AB$$?

(From Geometry, Unit 4, Lesson 3.)

### Problem 7

What is the length of the square’s side?

A:

3 units

B:

$\frac{6}{\sqrt2}$ units

C:

$6 \sqrt2$ units

D:

12 units

### Problem 8

Find the lengths of segments $$AD$$ and $$BD$$. Then check your answers using a different method.

(From Geometry, Unit 3, Lesson 13.)