# Lesson 10

Solving Problems with Trigonometry

### Problem 1

Technology required. Find the area of the isosceles trapezoid.

### Solution

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### Problem 2

Technology required. The sun is 62 degrees above the horizon. A tree casts a shadow that is 12 feet long. How tall is the tree?

### Solution

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### Problem 3

Technology required. A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.

1. How high is the plane at the time?
2. What is the distance of the plane’s path?

### Solution

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### Problem 4

Technology required. Find the missing measurements.

### Solution

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(From Unit 4, Lesson 9.)

### Problem 5

Technology required. Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees.

Is this a safe ramp? Explain or show your reasoning.

### Solution

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(From Unit 4, Lesson 9.)

### Problem 6

Select all true equations.

A:

$$\cos(37)=\sin(53)$$

B:

$$\tan(37)=\tan(53)$$

C:

$$\sin(37)=\cos(53)$$

D:

$$\sin(37)=\sin(53)$$

E:

$$\cos(\theta)=\sin(90-\theta)$$

### Solution

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(From Unit 4, Lesson 8.)

### Problem 7

Technology required. Clare is flying a kite. She gets tired, so she stakes the kite into the ground. The kite is on a string that is 30 ft long and makes a 27 degree angle with the ground. How high is the kite?

A:

30 ft

B:

13.6 ft

C:

26.7 ft

D:

15.3 ft

### Solution

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(From Unit 4, Lesson 7.)

### Problem 8

What is the length of the diagonal?