Question

The last question. I give all my points !!!

Traduction:
Calculate the perimeter of the polygon
where
a= 58°
b=C
A= 24.6

Options

A) 100.2 m
B) 96.4 m
C) 78.9 m

Answer 1

A) 100.2 m

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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