Question

The side upper A upper B is labeled c. The side upper A upper C is labeled b. The side upper B upper C is labeled a. A line labeled h connects the vertex upper B and the middle of the side upper A upper C and it forms a right angle with the edge.

If h=10
ℎ
=
10
meters and m∠C = 39°
𝑚
∠
𝐶

=

39
°
, then what is the length of side a
𝑎
? Round your answer to the nearest whole number.
13 meters
13 meters

8 meters
8 meters

16 meters
16 meters

6 meters

Answer 1

Place AC horizontally with its midpoint M at the origin and B at (0,h). Let AC = 2d, so C = (d,0) and B = (0,h). Then
cos ∠C = (CA·CB)/(|CA||CB|) = d / sqrt(d^2 + h^2).

With ∠C = 39° this gives d / sqrt(d^2 + h^2) = cos 39°, so
a = BC = sqrt(d^2 + h^2) = h / sin 39°.

Thus a = 10 / sin 39° ≈ 15.89 ≈ 16 meters.

Answer: 16 meters.