Answer:
Perimeter = 105 + 15√3 in
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