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.
![Car driving down right triangle ramp. Legs of right triangle are 15 and 95.](https://cms-im.s3.amazonaws.com/NPhtR5Jyie5tLJ1wyAfEwkyu?response-content-disposition=inline%3B%20filename%3D%22download%20%25281%2529.png%22%3B%20filename%2A%3DUTF-8%27%27download%2520%25281%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T001034Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=72df1e7d5a9006ba8b7c410a15e18b37f4d00414f9fe5670dc1f8a0c5a1f62a5)
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 \(BCA\).