Lesson 9

Using Trigonometric Ratios to Find Angles

View Student Lesson

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.

Solution

For access, consult one of our IM Certified Partners.

Problem 2

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

Rectangle A B C D with diagonal A C. AB is 3 units, B C is 12 units. Angle B A C is labeled alpha and A C B is labeled theta.

Solution

For access, consult one of our IM Certified Partners.

Problem 3

Technology required. Find the missing measurements. 

Right triangle abc. Side AB = 21 units, side CA= 35 units. Hypotenuse unknown 

Solution

For access, consult one of our IM Certified Partners.

Problem 4

Select all the true equations:

Right triangle A B C. A C is x units, B C is y units, A B is 15 units. Angle B A C is 27 degrees, angle A B C is 63 degrees, and angle A C B is 90 degrees.
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

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 7.)

Problem 7

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

Triangle D E F. Angle D is 40 degrees. Angle E is 50 degrees. Side D E is x. Side F D is 3.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 6.)

Problem 8

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

2 right triangles. On left, base = 3 units, height = x, hypotenuse = 5 units. On right, base = 9 units, height = 12 units, hypotenuse = y.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 1.)

Problem 9

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

Triangle ABC and ZXY.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 3.)