This document provides the step-by-step work to solve a trigonometry problem involving finding the length of an unknown side of a triangle. It uses trigonometric functions like sine, tangent, and cosine to relate known and unknown sides and angles. The problem involves finding the length of a roof at a 20 degree angle, then adjusting that angle by 6 degrees to get the final roof pitch of 24.4 degrees. Through multiple applications of trigonometric functions, the unknown adjacent side is calculated to be 10.87 inches.

1. Final Trig Problem Solution?
SolPowerPeople, Inc.
Austin, TX
March 10, 2012

2. Last Trig Problem

3. 24”
?
20°

4. opposite
sin(q )° =
24”
hypotenuse
opposite
sin(20)° =
? 24"
20° opposite
.342 =
24"
24 *.342 = opposite
8.2" = opposite

5. opposite
sin(q )° =
24”
hypotenuse
opposite
sin(20)° =
8.2” 24"
20°
opposite
.342 =
24"
24 *.342 = opposite
8.2" = opposite

6. Last Trig Problem

7. Angle of a 4/12 roof
Tangent of the angle is equal to the
4/12=rise/run opposite over the hypotenuse.
Therefore 4/12 = tangent of the angle
4”
4/12= 0.3333333
12” Arctan of 0.333333= 18.4°
(see earlier slideshow on “arctan”)

8. 6°
8.2”
18.4°

9. 6°
8.2” bring up by
Bring
down to roof pitch
zero° amount
18.4°

10. 8.2”
24.4°
(18.4° + 6°)

11. 8.2”
24.4°
?

12. opposite
tan(q )° =
adjacent
8.2"
tan(24.4)° =
adjacent
8.2"
.4536 =
adjacent
8.2"
adjacent =
.4536
adjacent = 18.077" 8.2”
24.4°
18.077”

13. adjacent
cos(q )° =
hypotenuse
adjacent
cos(53)° =
18.077" ?
adjacent 53° 18.077”
.6018 =
18.707"
18.077 *.6018 = adjacent
adjacent = 10.87"

14. adjacent
cos(q )° =
hypotenuse
adjacent
cos(53)° =
18.077" 10.87”
adjacent 53° 18.077”
.6018 =
18.707"
18.077 *.6018 = adjacent
adjacent = 10.87"