Question

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

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

Area of the triangle =1/2bh

A:68.7cm^2
B.161.7cm^2
c.381.3cm^2
D450.cm^2

Answer 1

you can start by finding the height or altitude ("alt" = vertical side touching hypotenuse and bottom base):
tangent (23) = opposite/adjacent (TOA), where opposite is altitude and adjacent is base
So tangent (23) = alt/27.6cm
alt = 27.6×tan23 = 27.6×0.424
alt = 11.72cm
So now area = 1/2 (b)(h), where h=alt
area = 1/2 (27.6cm)(11.72cm) = 161.7cm^2
$161.7{cm}^{2}$
So the correct answer is [B.]