Chapter 9.9, Problem 9PSB

a

To determine

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

Answer to Problem 9PSB

The value of $\cos \angle A=\frac{7}{25}$

Explanation of Solution

Given information:The following information has been given

  $AB=14$

  $AC=BC=25$

Formula used:Basic trigonometric identities have been used

Calculation:We apply the cosine formula in the triangle ADC where D is the midpoint of AB, we get

  $\cos \angle A=\frac{AD}{AC}$

Hence, we get

  $\cos \angle A=\frac{7}{25}$

b

To determine

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

Answer to Problem 9PSB

The value of $\sin \angle E=\frac{8}{17}$

Explanation of Solution

Given information:The following information has been given

  $ED=17$

  $DG=8$

Formula used:Basic trigonometric identities have been used

Calculation:we apply the cosine formula in the triangle RET, we get

  $\sin \angle E=\frac{DG}{DE}$

Hence, we get

  $\sin \angle E=\frac{8}{17}$

c

To determine

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

Answer to Problem 9PSB

The value of $\sin \angle DFG=\frac{4}{5}$

Explanation of Solution

Given information:The following information has been given

  $DF=10$

  $DG=8$

Formula used:Basic trigonometric identities have been used

Calculation:we apply the cosine formula in the triangle RET, we get

  $\sin \angle DFG=\frac{DG}{DF}$

Hence, we get

  $\sin \angle DFG=\frac{4}{5}$