Question

find the area of the given triangle. round your answer to the nearest tenth. do not round any intermediate computations. 18 48° square units

Explanation:

Step1: Identify triangle type and formula

This is a right - triangle. Let the base be \(b = 18\) and we need to find the height \(h\). We know that \(\tan(48^{\circ})=\frac{h}{18}\), so \(h = 18\times\tan(48^{\circ})\). The area of a right - triangle is \(A=\frac{1}{2}\times base\times height\), so \(A=\frac{1}{2}\times18\times(18\times\tan(48^{\circ})) = 9\times18\times\tan(48^{\circ})\).

Step2: Calculate the value

First, calculate \(\tan(48^{\circ})\approx1.1106\). Then, \(18\times\tan(48^{\circ})\approx18\times1.1106 = 19.9908\). Then, \(A=\frac{1}{2}\times18\times19.9908=9\times19.9908 = 179.9172\). Rounding to the nearest tenth, we get \(A\approx179.9\).

Answer:

\(179.9\)