# Lesson 5

Working with Ratios in Right Triangles

- Let’s solve problems about right triangles.

### Problem 1

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

- Verify this is a Pythagorean triple.
- 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.

Angle \(A\) is 20 degrees, \(BC\) is 2 units

\(AC\) is 7 units, \(BC\) is 3 units

Angle \(B\) is 50 degrees, \(BC\) is 4 units

Angle \(A\) is 30 degrees, \(BC\) is 5 units

\(AC\) 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?

27 degrees

30 degrees

60 degrees

63 degrees

### 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 |

\(C\) |

### Problem 6

What is the length of side \(AB\)?

### Problem 7

What is the length of the square’s side?

3 units

\(\frac{6}{\sqrt2}\) units

\(6 \sqrt2\) units

12 units

### Problem 8

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