Q23. - 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 $73.5$   square unit.

Step 1. Modify the given figure.

Draw the perpendicular$AE=h$

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 

$\begin{array}{l}\sin \theta =\frac{\text{Opposite}}{Hypotenuse}\\ \sin {50}^{\circ }=\frac{h}{8}\\ h=6.128\end{array}$

Step 3. Find the area of parallelogram.

Area of parallelogram can be found using the formula 

$\begin{array}{c}A=bh\\ =\left(12\right)\left(6.128\right)\\ =73.54\\ \approx 73.5\end{array}$

Therefore, the area of given figure is$73.5$ Square unit.