Chapter 9.9, Problem 7PSA

a

To determine

To find:The value of side BC .

Answer to Problem 7PSA

The value of $BC=2\sqrt{6}$

Explanation of Solution

Given information:The measures of following sides have been given

  $AB=7$

  $AC=5$

Formula used:Pythagoras theorem has been used.

Calculation:We apply the Pythagoras theorem in right triangle ABC, we get

  $5^2+B{C}^2=7^2$

Hence, we get

  $BC=2\sqrt{6}$

b

To determine

To find:The value of $\sin \angle A$

Answer to Problem 7PSA

The value of $\sin \angle A=\frac{2\sqrt{6}}{7}$

Explanation of Solution

Given information:The measures of following sides have been given

  $AB=7$

  $AC=5$

  $BC=2\sqrt{6}$

Formula used:Basic trigonometric identities are used

Calculation:We apply the sine formula in right triangle ABC, we get

  $\sin \angle A=\frac{BC}{AB}$

Hence, we get

  $\sin \angle A=\frac{2\sqrt{6}}{7}$

c

To determine

To find:The value of $\tan \angle B$

Answer to Problem 7PSA

The value of $\tan \angle B=\frac{2\sqrt{6}}{5}$

Explanation of Solution

Given information:The measures of following sides have been given

  $AB=7$

  $AC=5$

  $BC=2\sqrt{6}$

Formula used:Basic trigonometric identities have been used

Calculation:We apply the tangent formula in right triangle ABC, we get

  $\tan \angle B=\frac{BC}{AC}$

Hence, we get

  $\tan \angle B=\frac{2\sqrt{6}}{5}$