Find the perimeter of the trapezoid. Leave your answer in simples radical form

Perimeter = 105 + 15√3 in

Step-by-step explanation:

✔️Find the height of the trapezoid using trigonometric ratio:

Reference angle = 60°

opposite = height

Adj = 45 - 30 = 15 in

Thus:

Tan 60 = opp/adj

Tan 60 = height/15

height = 15*tan 60

height = 15√3 (tan 60 = √3)

✔️Find the slant height (hypotenuse) using Pythagorean Theorem:

Hypotenuse = √(height² + adj²)

Hypotenuse = √((15√3)² + 15²)

= √(675 + 225)

Hyp = √900

Hyp = 30

✔️Perimeter = 30 + 45 + 30 + 15√3

Perimeter = 105 + 15√3 in

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