3) Solve a right triangle that has a 40° angle and a 20 inch hypotenuse.

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section2.4: Applications
Problem 48PS: Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The...
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EXAMPLE 4
Solve a real-world problem
THEATER DESIGN Suppose your school is building a raked stage. The stage
will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle
of elevation) of 5° or less is generally preferred for the safety and comfort of
the actors. Is the raked stage you are building within the range suggested?
audience
stage back
30 ft
2 ft
stage front
Solution
Use the sine and inverse sine ratios to find the degree measure x of the rake.
sin x° =
opp.
- 2
= 0.0667
hyp.
30
x= sin 0.0667 = 3.824
The rake is about 3.8°, so it is within the suggested range of 5° or less.
A
raked stage slants upward from front to back to give the audience a better view.
Guided Practice Problem #3 and #4
3) Solve a right triangle that has a 40° angle and a 20 inch hypotenuse.
4) WHAT IF? In Example 4, suppose another raked stage is 20 feet long from front to back with
a total rise of 2 feet. Is this raked stage safe? Explain.
Transcribed Image Text:EXAMPLE 4 Solve a real-world problem THEATER DESIGN Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5° or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested? audience stage back 30 ft 2 ft stage front Solution Use the sine and inverse sine ratios to find the degree measure x of the rake. sin x° = opp. - 2 = 0.0667 hyp. 30 x= sin 0.0667 = 3.824 The rake is about 3.8°, so it is within the suggested range of 5° or less. A raked stage slants upward from front to back to give the audience a better view. Guided Practice Problem #3 and #4 3) Solve a right triangle that has a 40° angle and a 20 inch hypotenuse. 4) WHAT IF? In Example 4, suppose another raked stage is 20 feet long from front to back with a total rise of 2 feet. Is this raked stage safe? Explain.
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