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

63 yd²

Explanation:

Use the formula:

`\text{area of triangle} = (1)/(2) * \text{side}_1 * \text{side}_2 * \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} = (1)/(2) * \text{side}_1 * \text{side}_2 * \sin{(\text{includ\e ed angle})}`

`\text{area of triangle} = (1)/(2) * 14.5 \text{ yd} * 9 \text{ yd} * sin((106^\circ))`

`\text{area of triangle} = 65.25 * 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`