# Lesson 9

Using Trigonometric Ratios to Find Angles

- Let’s work backwards to find angles in right triangles.

### 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.

### Problem 2

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

### Problem 3

*Technology required. *Find the missing measurements.

### Problem 4

Select** all **the true equations:

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

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

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

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

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

### Problem 5

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

-30

30

60

180

### 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?

\(3.5 \tan(17)\)

\(3.5 \cos(17)\)

\(3.5 \sin(17)\)

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

### Problem 7

*Technology required. *What is the value of \(x\)?

### Problem 8

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

### Problem 9

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