Question

A rectangular field has a longer side of 100 meters. A diagonally path across the field makes an angle with the shorter side of 50° What is the perimeter of the field to the nearest meter? please show all work

Answer 1

368 m

Explanation:

The long side is opposite the 50° angle, and the short side is adjacent. Then the definition of the tangent ratio tells you ...

Tan = Opposite/Adjacent

tan(50°) = (100 m)/(short side)

Multiplying by (short side)/tan(50°) we get ...

short side = 100 m/tan(50°) ≈ 83.9 m

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The perimeter of the field is the sum of side lengths: two times the short side plus two times the long side:

P = 2(short side + long side) = 2(83.9 m +100 m) = 367.8 m

P ≈ 368 m

The perimeter of the field is about 368 meters.