Answer:
6.9 m
Explanation:
You want to know the length of segment x in the diagram shown.
Tangent
The tangent function relates the side lengths of a right triangle to the acute angle:
Tan = Opposite/Adjacent
If r represents the length of the bottom part of the right side of the triangle, we have ...
tan(28°) = r/(31 m)
tan(28° +9°) = (r +x)/(31 m)
Solution
Multiplying these equations by 31 m and solving for x gives ...
(31 m)·tan(28°) = r
(31 m)·tan(37°) = r +x
x = (31 m)·tan(37°) -(31 m)·tan(28°) = (31 m)·(tan(37°) -tan(28°))
x ≈ 6.9 m
The length x is about 6.9 meters.