Answer:
A) 100.2 m
Step-by-step explanation:
You want the perimeter of the right trapezoid shown with slant side A=24.6 m, acute angle α=58°, and the short base C equal in length to the height B.
Trig relations
If length C were reduced to zero, α would be an acute angle in a right triangle with opposite side B and adjacent side (D-C). The measures of those sides are found using trigonometric relations:
Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse × Sin
Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse × Cos
Application
B = C = (24.6 m)·sin(58°)
D-C = (24.6 m)·cos(58°)
The perimeter is ...
P = A + B + C + ((D-C) +C)
P = (24.6 m) + (24.6 m)·sin(58°) + (24.6 m)·sin(58°) + ((24.6 m)·cos(58°) +(24.6 m)·sin(58°))
P = (24.6 m)(1 + 3·sin(58°) +cos(58°)) ≈ 100.2 m
The perimeter of the polygon is about 100.2 m.
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