Question

3. Solve for the side length of BA and AC. * (image attached)

Answer 1

Ba = 8,ac = 16 is the correct one

Answer 2

Answer:

D. BA = 8, AC = 8√3

Step-by-step explanation:

First, because this is a right triangle, refer to the trigonometric ratios:

tangent = opposite side/adjacent side

sine = opposite side/hypotenuse

cosine = adjacent side/hypotenuse

BA is the opposite side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use sine:

sine = opposite side/hypotenuse

sin(30) = BA/16

sin(30) / 1 = BA / 16

Cross multiply:

BA = sin(30) (16)

BA = 8

AC is the adjacent side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use cosine:

cosine = adjacent side/hypotenuse

cos(30) = AC/16

cos(30) / 1 = AC / 16

Cross multiply:

AC = cos(30) (16)

AC = 8√3

You can check by using the Pythagorean Theorem:

a² + b² = c²

8² + (8√3)² = 16²

64 + 192 = 256

256 = 256