Question

Determine the area of the blue triangle below. Round your answer to the nearest tenth.

Answer 1

Answer:

68.9 in^2

Step-by-step explanation:

first lets find the height of the blue triangle

hypotenuse = 15 in

one side is 12 in whereas other has to be find.

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.76 = opposite/15

0.766*15 = opposite

11.49 = opposite

area of triangle = base*height/2

=12*11.49/2

=136.88/2

=68.94

=68.9 in^2

Answer 2

Answer:

A = 68.9 in²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ ab sinC ( a, b are 2 sides and C the angle between them )

Here a = 12, b = 15 and C = 50° , then

A = $\frac{1}{2}$ × 12 × 15 × sin50°

   = 6 × 15 × sin50°

   = 90 × sin50° ≈ 68.9 in² ( to the nearest tenth )