Chapter 11: Q22. (page 432)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Hypotenuse=10 and $θ = 54^{\circ}$

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

$\begin{array}{l} \cos θ = \frac{A d j a c e n t}{H y p o t e n u s e} \\ \cos 54^{\circ} = \frac{BC}{A C} \\ \cos 54^{\circ} = \frac{BC}{12} \\ B C = 7.0536 \end{array}$

Base $= 7.0536$

Step 3. Find the Height of triangle.

$\begin{array}{l} \tan 54^{\circ} = \frac{AB}{B C} \\ \tan 54^{\circ} = \frac{AB}{7.0536} \\ A B = 7.0536 \times 1.3764 \\ A B = 9.708 \end{array}$

Height $= 9.708$

Step 4. Find the area of triangle.

Area of triangle can be found using the formula

$\begin{matrix} A = \frac{1}{2} b h \\ = \frac{1}{2} (7.053) (9.708) \\ = 34.335 \\ \approx 34.3 \end{matrix}$

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Find the Height of triangle.

Step 4. Find the area of triangle.

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