Question

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

Explanation:

Step1: Find the shorter leg

In a \(30 - 60-90\) triangle, the side opposite the \(30^{\circ}\) angle (shorter leg) is half the hypotenuse.
If the hypotenuse \(c = 6\) ft, then the shorter leg \(a=\frac{c}{2}=\frac{6}{2}=3\) ft.

Step2: Find the longer leg

The longer leg \(b\) (opposite the \(60^{\circ}\) angle) in a \(30 - 60 - 90\) triangle is \(b = a\sqrt{3}\).
Since \(a = 3\) ft, \(b=3\sqrt{3}\approx3\times1.732 = 5.196\) ft.

Step3: Calculate the perimeter

The perimeter \(P\) of the triangle is \(P=a + b + c\).
Substitute \(a = 3\) ft, \(b\approx5.196\) ft, and \(c = 6\) ft.
\(P=3+5.196 + 6=14.196\approx14.2\) ft.

Answer:

B. \(14.2\) ft