Q24. - Geometry

Question

Use a calculator or the trigonometry table on page311  to find the area of each figure to the nearest tenth.

An isosceles triangle with a${32}^{\circ }$ ,vertex angle and a base of 8cm

Step-by-Step Solution

Answer

The area of given figure is approximately $16.96$   square unit.

Step 1. Analyze the given information.

Base=8 and $\theta ={32}^{\circ }$

Since in an isosceles triangle two sides are equal in length, then we get two sides of triangle are $8,8$

Step 2. Concept Used.

Here, we shall use the formula

$A=\frac{1}{2}absin\theta$

Where a.b are the sides of triangle and $\theta$ is angle between them.

Step 3. Find the area of triangle.

So, the area of triangle 

$\begin{array}{c}A=\frac{1}{2}\left(8\right)\left(8\right)sin{32}^{\circ }\\ =4\times 8\times 0.53\\ \approx 16.96\end{array}$

Therefore, the area of given figure is $16.96$Square unit.