Question

if the area △ABC=134 square feet, m∠C=41 degrees, and b=24 feet, then what is the length of side a? round your answer to the nearst whole number.

Answer 1

In a triangle, the area is given by the formula:

Area = ½ * base * height

Where base is the length of one of the sides and height is the perpendicular distance from the base to the opposite vertex.

Using this formula, we have:

134 = ½ * 24 * height

Simplifying:

134 = 12 * height

Dividing both sides by 12:

11.167 = height

Now, we can apply the trigonometric relationship in a right-angled triangle to find the length of side a.

In right triangle ABC, we have:

sin(C) = opposite/hypotenuse

sin(41 degrees) = height/a

Solving for a:

a = height / sin(41 degrees) = 11.167 / sin(41 degrees)

Using a calculator:

a ≈ 17.428

Rounding to the nearest whole number:

a ≈ 17

Therefore, the length of side a is approximately 17 feet.