Question

select the correct answer.
lacy is making a new sail for her boat. the sail needs to have the given dimensions.
approximately how much fabric does she need for the sail?
a. 70.1 square feet
b. 99.2 square feet
c. 140.3 square feet
d. 81 square feet

Explanation:

Step1: Find shorter leg length

In a 30-60-90 triangle, the shorter leg (opposite 30°) is half the hypotenuse:
$\text{Shorter leg} = \frac{18}{2} = 9$ ft

Step2: Find longer leg length

The longer leg (opposite 60°) is shorter leg times $\sqrt{3}$:
$\text{Longer leg} = 9\sqrt{3} \approx 15.588$ ft

Step3: Calculate triangle area

Area of right triangle is $\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$:
$\text{Area} = \frac{1}{2} \times 9 \times 9\sqrt{3} = \frac{81\sqrt{3}}{2} \approx 70.1$ square feet

Answer:

A. 70.1 square feet