Right triangle upper A upper B upper C has a small square box at angle B. The side opposite of each angle is labeled as the lowercase letter of the angle name.
Use the Law of Sines to solve the following problem. If ∠C=62 degrees
and side c=16 cm
, then what is the length of side a? Round your answer to the nearest centimeter.
(1 point)
cm
To use the Law of Sines, we will set up the following proportion:
sin(A) / a = sin(C) / c
We are given that ∠C = 62 degrees and side c = 16 cm.
First, we need to find the measure of ∠A since the sum of angles in a triangle is 180 degrees.
∠A = 180 - 90 - 62 = 28 degrees
Now we can plug in the values into the equation:
sin(28) / a = sin(62) / 16
To find the length of side a, we can rearrange the equation:
a = 16 * sin(28) / sin(62)
a = 16 * 0.4695 / 0.8829
a = 8.52 cm
Therefore, the length of side a is approximately 9 cm when rounded to the nearest centimeter.