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.



In △ABC, if a=36 cm and m∠C = 23°, then what is the length of altitude h? Round your answer to the nearest whole number.

(1 point)
Responses

92 cm
92 cm

33 cm
33 cm

14 cm
14 cm

39 cm

Answer 1

If the perpendicular from B meets AC at its midpoint, then BA = BC (B lies on the perpendicular bisector of AC), so triangle ABC is isosceles and ∠A = ∠C = 23°. Drop BM to the midpoint M of AC; triangle ABM is right at M and has hypotenuse AB = 36 and angle A = 23°, so

h = BM = AB · sin(23°) = 36 · sin 23° ≈ 36 · 0.3907 ≈ 14.07 cm.

Rounded to the nearest whole number: 14 cm.