Question

Use the Law of Sines to solve the following problem. If
and side
, howlong is side
a
to the nearest yard?
(1 point)
∠C = 35 degrees c = 42 yd.
29 yd.
43 yd.
60 yd.
64 yd.

Answer 1

It looks like part of the problem is missing — to use the Law of Sines you need an angle opposite side a (∠A). The general formula is

a = c * sin(A) / sin(C) = 42 * sin(A) / sin(35°).

If you give me ∠A I’ll compute a and pick the nearest yard. (If you intended ∠A = 36°, then a = 42*(sin 36°)/(sin 35°) ≈ 43 yd.)

For reference, here are the angles ∠A that would correspond to each answer choice (using sin35° ≈ 0.573576):

- a = 29 yd → sin A = 29·sin35°/42 ≈ 0.3960 → A ≈ 23.3°
- a = 43 yd → sin A = 43·sin35°/42 ≈ 0.5873 → A ≈ 36.0°
- a = 60 yd → sin A = 60·sin35°/42 ≈ 0.8194 → A ≈ 55.0°
- a = 64 yd → sin A = 64·sin35°/42 ≈ 0.8740 → A ≈ 61.0°

Tell me ∠A (or confirm which of these angles was given) and I’ll finish it.