If x = 39, y = 58, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.

Question

triangles ABC and ADC in which angle C is a right angle, point D is on segment BC between points B and C, the measure of angle ABD is x degrees, and the measure of angle ADC is y degrees

0.74 units
1.17 units
1.64 units
2.14 units

Answer 1

To find the lengths of segments AB and AD, we can use the sine ratio in triangle ABC and triangle ADC.

In triangle ABC:
sin(x) = AC / AB
sin(39) = 4 / AB
AB = 4 / sin(39) ≈ 6.35 units

In triangle ADC:
sin(y) = AC / AD
sin(58) = 4 / AD
AD = 4 / sin(58) ≈ 3.17 units

The difference in length between segments AB and AD is:
AB - AD = 6.35 - 3.17 = 3.18 units

Rounded to the nearest hundredth, the difference is 3.18 units, which is closest to 3.17 units. Therefore, the answer is 3.17 units.