Question

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. 81 square feet c. 140.3 square feet d. 99.2 square feet

Explanation:

Step1: Find the base and height of the triangle

In a 30 - 60 - 90 triangle, if the hypotenuse $c = 18$ ft. The side opposite the 30 - degree angle (the shorter leg) $a=\frac{c}{2}=9$ ft, and the side opposite the 60 - degree angle (the longer leg) $b = 9\sqrt{3}$ ft. We can take the base $b_1=9$ ft and height $h = 9\sqrt{3}$ ft.

Step2: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Substitute $b_1 = 9$ ft and $h = 9\sqrt{3}$ ft into the formula: $A=\frac{1}{2}\times9\times9\sqrt{3}=\frac{81\sqrt{3}}{2}\approx\frac{81\times1.732}{2}=\frac{140.292}{2}=70.146\approx70.1$ square feet.

Answer:

A. 70.1 square feet