Question

select the correct answer.
freda waves a small flag pennant when her favorite baseball player hits a grand slam.
approximately how much fabric, in square inches, is used to make up the flag on her pennant?
43.3
21.65
17.68
23.67

Explanation:

Step1: Identify triangle type & sides

This is a 30-60-90 right triangle. The hypotenuse is 10 in. In such a triangle, the shorter leg (opposite 30°) is $\frac{1}{2} \times \text{hypotenuse} = 5$ in, and the longer leg (opposite 60°) is $5\sqrt{3}$ in.

Step2: Calculate triangle area

Use area formula for right triangle: $\text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$
$\text{Area} = \frac{1}{2} \times 5 \times 5\sqrt{3} = \frac{25\sqrt{3}}{2}$

Step3: Compute approximate value

Substitute $\sqrt{3} \approx 1.732$:
$\text{Area} \approx \frac{25 \times 1.732}{2} = \frac{43.3}{2} = 21.65$

Answer:

21.65