Lesson 10 Using Trigonometric Relationships Practice Understanding

Ready

Based on each set of similar triangles or parallel lines, create a proportion and solve it to find the missing values.

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Set

Solve each right triangle. Give any missing sides and missing angles.

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Use trigonometric ratios and the Pythagorean theorem to solve each problem.

9.

Jack is looking up the hill at Jill and wondering how much vertical increase there actually is from his position to her position on the hill. They know there is a $15 °$ angle of incline, and Jack measures as he goes to meet Jill that he has gone $30 yards$ . Calculate the vertical distance.

10.

Kim is trying to use the shadow of a large tree to measure the height of the tree. The length of the shadow has been measured as $20 feet$ and the angle of incline has been measured as $50 °$ . How tall is the tree?

Model each of the situations with a right triangle and then solve the triangle to find the desired values.

11.

Alex is standing on the top of a building looking out at a boat in the lake. The distance from the top of the building to the ground is $150 feet$ , and Alex is able to measure the angle from vertical to the line of sight as $70 °$ . How far from the base of the building is the boat?

Solution:

12.

The altitude of a plane is $6,000 feet$ and the angle of descent to the landing strip is $3 °$ . How much distance will the plane actually travel in its path through the air before it touches down?

Solution:

Use the given trigonometric ratio, which is based on actual side length measures, to sketch a right triangle and solve the triangle.

13.

$\sin (A) = \frac{1}{2}$

Solution:

Sketch:

14.

$\cos (B) = \frac{3}{5}$

Solution:

Sketch:

15.

$\tan (B) = \frac{6}{7}$

Solution:

Sketch:

16.

$\sin (B) = \frac{7}{10}$

Solution:

Sketch:

Go

Sketch a drawing of the situation, then solve each problem.

17.

Mark is building his son a pitcher’s mound so he can practice for his upcoming baseball season in the backyard. Mark knows the league requires an incline of $12 °$ and an elevation of $8 inches$ in height. How long will the front of the pitcher’s mound need to be?

Solution:

Sketch:

18.

Susan is designing a wheelchair ramp. Wheelchair ramps require a slope that is no more than $1$ inch of rise for every $12$ inches of horizontal distance. Susan wants to determine how much horizontal distance a ramp of $6 feet$ in length will span. She also wants to know the degree of incline from the base of the ramp to the ground.

Solution:

Sketch:

19.

Michael is designing a house with a roof pitch of $5$ . Roof pitch is the number of inches a roof will rise for every $12 inches$ of run. What is the angle that will need to be used in building the trusses and supports for the roof? At the peak of the roof, what angle will there be when the front and the back of the roof come together?

Solution:

Sketch: