Question

Howard is trying to find the area of a triangle with side lengths 5, 12, and 14 inches, and an angle measuring 20°. He constructs an altitude to the 14-inch side, forming two right triangles as shown in the following diagram.

Answer 1

The formula for determining the area of a triangle is expressed as

Area = 1/2 * base * height

We don't know the height, h. I would draw triangle below that would make the illustration clearer

Considering traingle ADC with angle 20 as the reference angle,

AC = 12 = hypotenuse

h = opposite side

We would find h by applying the Sine trigonometric ratio which is expressed as

Sin# = opposite side/hypotenuse

# = 20

Thus,

Sin20 = h/12

h = 12Sin20 = 12 * 0.342

h = 4.104

base = 14

Thus, area = 1/2 * 14 * 4.104

Area = 28.73 square inches