Question

select the correct answer.
tobias wants to add a wooden trim to a triangular window with the dimensions shown.
what is the approximate length of wood needed to trim the window?
a. 14.5 ft
b. 14.2 ft
c. 15.4 ft
d. 13.2 ft

Explanation:

Step1: Use the properties of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the hypotenuse \(c = 6\) ft, then the side opposite the 30° angle \(a=\frac{c}{2}\). So \(a = \frac{6}{2}=3\) ft.

Step2: Find the side opposite the 60° angle

The side opposite the 60° angle \(b=a\sqrt{3}\). Substituting \(a = 3\) ft, we get \(b = 3\sqrt{3}\approx3\times1.732 = 5.196\) ft.

Step3: Calculate the perimeter

The perimeter \(P=a + b + c\). Substituting \(a = 3\) ft, \(b\approx5.196\) ft, and \(c = 6\) ft, we have \(P=3+5.196 + 6=14.196\approx14.2\) ft.

Answer:

B. 14.2 ft