Q21. - Geometry

Question

Use a calculator or the trigonometry table on page 311 to find the area of each figure to the nearest tenth.

Step-by-Step Solution

Answer

The area of given figure is approximately $18.2$   square unit.

Step 1. Given information.

Adjacent=10 and $\theta ={20}^{\circ }$

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 

$\begin{array}{l}tan\theta =\frac{\text{Opposite}}{Adjacent}\\ tan{20}^{\circ }=\frac{\text{AB}}{BC}\\ tan{20}^{\circ }=\frac{\text{AB}}{10}\\ AB=3.6397\end{array}$

Step 3. Find the area of triangle.

Area of triangle can be found using the formula 

$\begin{array}{c}A=\frac{1}{2}bh\\ =\frac{1}{2}\left(10\right)\left(3.6397\right)\\ =18.1985\\ \approx 18.2\end{array}$

Therefore, the area of given figure is $18.2$Square unit.