In ΔVWX, the measure of ∠X=90°, the measure of ∠W=20°, and XV= 58 feet. Find the length of VW to the nearest tenth of a foot.

Question

Using trig to find a side

Answer 1

XV is opposite angle W, and VW is opposite angle X. Angle X has measure 90 degrees, and angle W has measure 20 degrees. Thus, as XV = 58, we can either use the sin law and say that XV/VW = sin 20°/sin 90°, so VW = XV sin 90°/sin 20°= 58 * 1/0.342020143325669 = 169.6 feet or use the fact that this is a right triangle to say that VW = XV csc 20° = 58 csc 20° = 169.6.