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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q21. (page 432)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Adjacent=10 and $θ = 20^{\circ}$

02

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

$\begin{array}{l} t a n θ = \frac{Opposite}{A d j a c e n t} \\ t a n 20^{\circ} = \frac{AB}{B C} \\ t a n 20^{\circ} = \frac{AB}{10} \\ A B = 3.6397 \end{array}$

03

Step 3. Find the area of triangle.

Area of triangle can be found using the formula

$\begin{matrix} A = \frac{1}{2} b h \\ = \frac{1}{2} (10) (3.6397) \\ = 18.1985 \\ \approx 18.2 \end{matrix}$

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

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