Chapter 9.10, Problem 11PSB

a

To determine

To find:The value of the base angles to the nearest degree

Answer to Problem 11PSB

The value of the base angles is $x={67}^0$ each

Explanation of Solution

Given information:The following information has been given

Legs of isosceles triangle are $18$ each

The base is $14$

Formula used:Basic trigonometric identities have been used

Calculation:We know that if we draw an altitude from the vertex to the base, a right triangle will be formed. Now, we assume the base angles to be of value x each. Hence, in this right triangle, we can say that

  $\cos x=\frac{7}{18}$

Thus, we can say that

  $x={\cos }^{-1}\left(\frac{7}{18}\right)$

Now, from the table of trigonometric values, we can say that

  ${\cos }^{-1}\frac{7}{18}={67.11}^0$

Thus, we can say that

  ${67.11}^0=x$

Hence, rounding off this value to the nearest degree, we get

  $x={67}^0$

b

To determine

To find:The exact value of the altitude.

Answer to Problem 11PSB

The value of the altitude is $y=16.583$

Explanation of Solution

Given information:The following information has been given

Legs of isosceles triangle are $18$ each

The base is $14$

Formula used:Pythagoras theorem has been used

Calculation:We know that if we draw an altitude from the vertex to the base, a right triangle will be formed. Now, we assume the altitude to be of value y .

Hence, in this right triangle, we apply the Pythagoras theorem. Thus, we get

  $7^2+y^2={18}^2$

Thus, we can say that

  $y=5\sqrt{11}$

Hence, for the exact value, wee can say that

  $y=16.583$