Answer:
Explanation:
To find the measure of length BC, we need to use the information provided in the image.
Looking at the image, we see that angle BAC is labeled as 93 degrees and angle ACB is not labeled.
However, we can determine the measure of angle ACB by using the fact that the sum of the angles in a triangle is always 180 degrees.
So, to find the measure of angle ACB, we can subtract the measures of angles BAC and ABC from 180 degrees.
→ 180 - 93 - 58 = 29 degrees.
Now that we have the measure of angle ACB, we can use it to find the length of side BC. Since angle ACB is opposite side BC, we can use the sine ratio (SOH) to calculate BC.
The sine ratio states that 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, BC is the opposite side and AC is the hypotenuse.
Using the sine ratio:
→ sin(ACB) = BC / AC.
→ sin(29) = BC / 16 .
To find BC, we can multiply both sides of the equation by 16:
→ 16 * sin(29) = BC .
Using a calculator, we can evaluate sin(29) to be approximately 0.4848:
→ 16 * 0.4848 = BC BC ≈ 7.758 .
Therefore, the measure of length BC is approximately 7.758. Therefore, the correct answer is option a. 19.