Chapter 10: Q66. (page 660)

Find the values of the three trigonometric ratios for angle A.

Short Answer

Expert verified

The values of the three trigonometric ratios for angle A are $\sin (∠ A) = \frac{4}{5}$ , $\cos (∠ A) = \frac{3}{5}$ and $\tan (∠ A) = \frac{4}{3}$ .

Step by step solution

Step 1. Given.

The values of the three trigonometric ratios are given.

Step 2. Write the formulas for the trigonometric ratios.

The formula for the trigonometric ratios is:

$\sin (∠ A) = \frac{legopposite ∠ A}{hypotenuse}$

$\cos (∠ A) = \frac{legadjacentto ∠ A}{hypotenuse}$

$\tan (∠ A) = \frac{legopposite ∠ A}{legadjacentto ∠ A}$

Step 3. Find the values of the three trigonometric ratios for angle A.

The given diagram is:

From the diagram, it can be noticed that the leg opposite $∠ A$ , leg adjacent to $∠ A$ , and the hypotenuse are 4, 3, and 5 respectively.

Therefore,

$\sin (∠ A) = \frac{legopposite ∠ A}{hypotenuse} = \frac{4}{5}$

$\cos (∠ A) = \frac{legadjacentto ∠ A}{hypotenuse} = \frac{3}{5}$

$\tan (∠ A) = \frac{legopposite ∠ A}{legadjacentto ∠ A} = \frac{4}{3}$

Therefore, the values of the three trigonometric ratios for angle A are $\sin (∠ A) = \frac{4}{5}$ , $\cos (∠ A) = \frac{3}{5}$ and $\tan (∠ A) = \frac{4}{3}$ .

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Find the values of the three trigonometric ratios for angle A.

Short Answer

Step by step solution

Step 1. Given.

Step 2. Write the formulas for the trigonometric ratios.

Step 3. Find the values of the three trigonometric ratios for angle A.

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