Question

Given ABC; angle B = 75 degrees, CB = 7in, and BA = 9in. Find the area of triangle ABC.

A) 27 square inches
B) 36 square inches
C) 45 square inches
D) 54 square inches

Answer 1

To find the area of triangle ABC, use the formula for the area of a triangle: Area = 1/2 * base * height. Use trigonometry to find the height of the triangle and substitute it into the area formula.

Step-by-step explanation:

To find the area of triangle ABC, we can use the formula for the area of a triangle: Area = 1/2 * base * height.

Since angle B is given as 75 degrees and CB is given as 7 inches, we can use trigonometry to find the height of the triangle. The height (BC') of the triangle can be calculated using the formula BC' = CB * sin(B).

Therefore, BC' = 7 * sin(75) inches. Once we have the height, we can substitute it into the area formula to find the area of the triangle: Area = 1/2 * 9 * (7 * sin(75)). Calculate the value to get the final answer.