# Lesson 5

Working with Ratios in Right Triangles

### 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.

### Solution

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### 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?

### Solution

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### 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

### Solution

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### 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

### Solution

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(From 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
$$C$$

### Solution

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(From Unit 4, Lesson 4.)

### Problem 6

What is the length of side $$AB$$?

### Solution

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(From 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

### Solution

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### Problem 8

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