Question

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.

What is the approximate area of the triangle? Round to the nearest tenth.

Area of a triangle = One-halfbh

68.7 cm2
161.8 cm2
381.3 cm2
450.0 cm2

Answer 1

Adjacent = 27.6 = 30·cos23°, so the opposite leg = 30·sin23° ≈ 30(0.390731) = 11.7219 cm.

Area = 1/2 · (adjacent) · (opposite) = 0.5 · 27.6 · 11.7219 ≈ 161.8185 ≈ 161.8 cm².

Answer: 161.8 cm².