Question

find the area of the given triangle.
round your answer to the nearest tenth. do not round any intermediate computations.
14
38°
square units

Explanation:

Step1: Identify triangle type and formula

This is a right - triangle. The area of a right - triangle is given by \(A=\frac{1}{2}\times base\times height\). We know the base is 14, and we need to find the height. Let the height be \(h\). In a right - triangle, \(\tan(\theta)=\frac{opposite}{adjacent}\). Here, \(\theta = 38^{\circ}\), adjacent side (base) \(= 14\), and opposite side is the height \(h\). So \(\tan(38^{\circ})=\frac{h}{14}\), which means \(h = 14\times\tan(38^{\circ})\).

Step2: Calculate the height

We know that \(\tan(38^{\circ})\approx0.7813\) (using a calculator). So \(h = 14\times0.7813=10.9382\).

Step3: Calculate the area

Using the area formula for a right - triangle \(A=\frac{1}{2}\times base\times height\). Substitute base \( = 14\) and height \(h = 10.9382\) into the formula. \(A=\frac{1}{2}\times14\times10.9382=7\times10.9382 = 76.5674\). Rounding to the nearest tenth, we get \(A\approx76.6\).

Answer:

\(76.6\)