# Lesson 9

Using Trigonometric Ratios to Find Angles

### Problem 1

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 ramp safe? If not, provide dimensions that would make the ramp safe.

### Solution

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### Problem 2

Technology required. $$ABCD$$ is a rectangle. Find the length of $$AC$$ and the measures of $$\alpha$$ and $$\theta$$

### Solution

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### Problem 3

Technology required. Find the missing measurements.

### Solution

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### Problem 4

Select all the true equations:

A:

$$\sin(27) =\frac{x}{15}$$

B:

$$\cos(63) =\frac{y}{15}$$

C:

$$\tan(27) = \frac{y}{x}$$

D:

$$\sin(63) = \frac{x}{15}$$

E:

$$\tan(63) = \frac{y}{x}$$

### Solution

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(From Unit 4, Lesson 8.)

### Problem 5

What value of $$\theta$$ makes this equation true? $$\sin(30)=\cos(\theta)$$

A:

-30

B:

30

C:

60

D:

180

### Solution

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(From Unit 4, Lesson 8.)

### Problem 6

A rope with a length of 3.5 meters is tied from a stake in the ground to the top of a tent. It forms a 17 degree angle with the ground. How tall is the tent?

A:

$$3.5 \tan(17)$$

B:

$$3.5 \cos(17)$$

C:

$$3.5 \sin(17)$$

D:

$$\frac{\sin(17)}{3.5}$$

### Solution

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(From Unit 4, Lesson 7.)

### Problem 7

Technology required. What is the value of $$x$$

### Solution

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(From Unit 4, Lesson 6.)

### Problem 8

Find the missing side in each triangle using any method. Check your answers using a different method.

### Solution

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(From Unit 4, Lesson 1.)

### Problem 9

The triangles are congruent. Write a sequence of rigid motions that takes triangle $$XYZ$$ onto triangle $$BCA$$.

### Solution

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(From Unit 2, Lesson 3.)