# Lesson 10

Solving Problems with Trigonometry

- Let’s solve problems about right triangles.

### Problem 1

*Technology required. *Find the area of the isosceles trapezoid.

### 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?

### Problem 3

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

- How high is the plane at the time?
- What is the distance of the plane’s path?

### Problem 4

*Technology required. *Find the missing measurements.

### 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.

### Problem 6

Select **all** true equations.

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

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

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

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

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

### 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?

30 ft

13.6 ft

26.7 ft

15.3 ft

### Problem 8

What is the length of the diagonal?