Trignometry Question Please help
1 answer:
Answer:
19.45°
Step-by-step explanation:
Suppose the post is 1 unit high. Then the distance from the post to another corner of the rectangle will satisfy the relation ...
distance/1 = tan(90° -angle of elevation)
So, for the near corner, the distance from the post is ...
distance = tan(90° -36°) = tan(54°) = 1.37638 . . . post lengths
For the other given corner, the distance from the post is ...
distance = tan(90° -22°) = tan(68°) = 2.47509 . . . post lengths
The Pythagorean theorem can be used to find the distance from the post to the diagonally opposite corner:
distance^2 = 1.37638^2 +2.47509^2 = 8.02048
distance = √8.02048 ≈ 2.83205
The relation of this to the angle of elevation is ...
tan(angle of elevation) = 1/2.83205
angle of elevation = arctan(1/2.83205) ≈ 19.45°
_____
In the attached diagram, we have used segments BP and CP as surrogates for the post, so we could determine distances PD and PE that are the sides of the rectangular courtyard. Then the courtyard diagonal is PF. Using PA as a surrogate for the post, we found the angle of elevation from F to A (the top of the post) to be 19.45°, as computed above.
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