Question

Use a calculator or the trigonometry table on page311to find the area of each figure to the nearest tenth.

Short answer

The area of given figure is approximately $34.3$ square unit.

Step-by-step solution

Step 1. Given information.

Hypotenuse=10 and$\theta ={54}^{\circ }$

Step 2. Concept Used.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Use trigonometric Ratios

$\begin{array}{l}\cos \theta =\frac{Adjacent}{Hypotenuse}\\ \cos {54}^{\circ }=\frac{\text{BC}}{AC}\\ \cos {54}^{\circ }=\frac{\text{BC}}{12}\\ BC=7.0536\end{array}$

Base$=7.0536$

Step 3. Find the Height of triangle.

$\begin{array}{l}\tan {54}^{\circ }=\frac{\text{AB}}{BC}\\ \tan {54}^{\circ }=\frac{\text{AB}}{7.0536}\\ AB=7.0536\times 1.3764\\ AB=9.708\end{array}$

Height$=9.708$

Step 4. Find the area of triangle.

Area of triangle can be found using the formula

$\begin{array}{c}A=\frac{1}{2}bh\\ =\frac{1}{2}\left(7.053\right)\left(9.708\right)\\ =34.335\\ \approx 34.3\end{array}$

Therefore, the area of given figure is $34.2$Square unit.