Question

tobias wants to add a wooden trim to a triangular window with the dimensions shown.
triangle image: right triangle, angle 30°, angle 60°, hypotenuse 6 ft
what is the approximate length of wood needed to trim the window?
a. 15.4 ft
b. 14.5 ft
c. 14.2 ft
d. 13.2 ft

Explanation:

Step1: Identify triangle type

It's a 30-60-90 right triangle with hypotenuse = 6 ft.

Step2: Find short leg

Short leg = hypotenuse × 0.5 = 6 × 0.5 = 3 ft.

Step3: Find long leg

Long leg = hypotenuse × $\frac{\sqrt{3}}{2}$ = 6 × $\frac{\sqrt{3}}{2}$ ≈ 5.196 ft.

Step4: Calculate perimeter

Perimeter = 6 + 3 + 5.196 ≈ 14.196 ft ≈ 14.2 ft? Wait, correction: Wait, hypotenuse is opposite right angle. Wait 30-60-90: sides opposite 30°,60°,90° are x, x√3, 2x. If hypotenuse (opposite 90°) is 6 ft, then 2x=6 → x=3 ft (opposite 30°). Side opposite 60° is x√3=3√3≈5.196 ft. Sum: 3+5.196+6≈14.196≈14.2 ft? But wait, maybe hypotenuse is 6 ft? Wait the figure shows the side opposite 60° is 6 ft? Wait no, original figure: angle 30°, angle 60°, right angle. The side labeled 6 ft is between 30° and 60°? No, wait the side labeled 6 ft is the hypotenuse? Wait if the side opposite 30° is 6 ft, then hypotenuse=12 ft, side opposite 60°=6√3≈10.392 ft. Perimeter=6+10.392+12≈28.392, not option. So correct: hypotenuse is 6 ft. Then sides are 3, 5.196,6 → sum≈14.2 ft (option C). Wait but earlier miscalculation. Wait the options: C is 14.2 ft. So answer is C. 14.2 ft.

Wait correction: The correct calculation: 30-60-90 triangle, hypotenuse=6 ft. Then legs: 3 ft (30° opposite) and 3√3≈5.196 ft (60° opposite). Sum: 3+5.196+6=14.196≈14.2 ft. So answer is C. 14.2 ft.

Step1: Recognize triangle type

30-60-90 right triangle, hypotenuse=6 ft.

Step2: Find short leg

Short leg = 6×0.5=3 ft.

Step3: Find long leg

Long leg = 6×(√3/2)≈5.196 ft.

Step4: Calculate perimeter

Perimeter=3+5.196+6≈14.2 ft.

Answer:

A. 15.4 ft