Question

select the correct answer.
rounded to the nearest tenth, what is the area of rectangle abcd?
a
b
30°
60°
9 ft
60°
30°
c
d
a. 70.1 square feet
b. 40.5 square feet
c. 35.1 square feet
d. 25.5 square feet
e. 24.6 square feet

Explanation:

Step1: Find length of AB (adjacent to 30°)

Use cosine: $\cos(30^\circ) = \frac{AB}{AD}$
$AB = 9 \times \cos(30^\circ) = 9 \times \frac{\sqrt{3}}{2} \approx 7.794$ ft

Step2: Find length of BD (opposite to 30°)

Use sine: $\sin(30^\circ) = \frac{BD}{AD}$
$BD = 9 \times \sin(30^\circ) = 9 \times \frac{1}{2} = 4.5$ ft

Step3: Calculate area of rectangle

Area = $AB \times BD$
$\text{Area} \approx 7.794 \times 4.5 \approx 35.1$ square feet

Answer:

C. 35.1 square feet