Question

Given a triangle with two sides that measure 14.5 yd and 9 yd and an included angle of 106°, find the area of the triangle. Round your answer to the nearest whole square yard.

Answer 1

Answer:

63 yd²

Step-by-step explanation:

Use the formula:

$\text{area of triangle} = \frac{1}{2} \times \text{side}_1 \times \text{side}_2 \times \sin{(\text{includ\e ed angle})}$

Given:

side₁ = 14.5 yd

side₂ = 9 yd

included angle = 106°

Insert values in formula.

$\text{area of triangle} = \frac{1}{2} \times \text{side}_1 \times \text{side}_2 \times \sin{(\text{includ\e ed angle})}$

$\text{area of triangle} = \frac{1}{2} \times 14.5 \text{ yd} \times 9 \text{ yd} \times \sin{(106^\circ)}$

$\text{area of triangle} = 65.25 \times \sin{(106^\circ)} \text{ yd}^2$

$\text{area of triangle} \approx 62.7222 \text{ yd}^2$

Rounded to the nearest whole square yard:

$\text{area of triangle} = 63 \text{ yd}^2$