Question

Question:

46 of 55
to nex
question mination
In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If
sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?

Answer 1

In a right triangle with angle B as a right angle, if sin(A) = 0.5 and side BC is 8 inches long, the length of side AC is 8 * sqrt(5) inches.

Step-by-step explanation:

In a right triangle, the sine of angle A is defined as the ratio of the length of the side opposite angle A to the length of the hypotenuse. In this case, sin(A) = AB/AC = 0.5.

Since angle B is a right angle, side AB is the side opposite angle A and side BC is the hypotenuse. Therefore, AB = 0.5 * BC = 0.5 * 8 = 4 inches.

Using the Pythagorean theorem, we can find the length of side AC:

AC^2 = AB^2 + BC^2 = 4^2 + 8^2 = 16 + 64 = 80

AC = sqrt(80) = 8 * sqrt(5) inches

Learn more about Geometry