Question

A carpenter needs to cut a small triangular piece of wood for part of a jewelry box. He knows the dimension shown and that θ=52°. What is the length of a to the nearest tenth of an inch?

Answer 1

To find the length of side 'a' in the small triangular piece of wood, we can use the sine function. The length of 'a' is approximately 9.04 inches.

Step-by-step explanation:

To find the length of side 'a' in the small triangular piece of wood, we can use the sine function. The sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is 'a' and the hypotenuse is 12. So, we have the equation sin(52°) = a/12. Solving for 'a', we get a = 12 * sin(52°). Calculating this value to the nearest tenth of an inch, we find that the length of 'a' is approximately 9.04 inches.