Chapter 6.1, Problem 45E

(a)

To determine

The equation that can be used to find the height of the tree in the given figure.

Answer to Problem 45E

The equation to find h is $h=40\times \frac{\sin {30}^0}{\sin {56}^0}$

Explanation of Solution

Given information:

The tree grew so that it was leaning $4^0$ from the vertical, at a point 40 meters from the tree, the angle of elevation to the top of the tree is ${30}^0$ .

Formula used:

Law of sines

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Calculation:

Given that

We need to find an equation for h that is b We have

  $\begin{array}{l}\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{b}{\sin {30}^0}=\frac{c}{\sin C}\\ C={180}^0-({30}^0+{94}^0)={56}^0\\ \frac{h}{\sin {30}^0}=\frac{40}{\sin {56}^0}\\ h=40\times \frac{\sin {30}^0}{\sin {56}^0}\end{array}$

The equation to find h is $h=40\times \frac{\sin {30}^0}{\sin {56}^0}$

Conclusion:

Thus, theequation to find h is $h=40\times \frac{\sin {30}^0}{\sin {56}^0}$

(b)

To determine

The height of the tree in the given figure.

Answer to Problem 45E

The height of tree is $24.12m$

Explanation of Solution

Formula used:

Law of sines

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Calculation:

Given that

We need to find height of tree, h that is b We have

  $\begin{array}{l}\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{b}{\sin {30}^0}=\frac{c}{\sin C}\\ C={180}^0-({30}^0+{94}^0)={56}^0\\ \frac{h}{\sin {30}^0}=\frac{40}{\sin {56}^0}\\ h=40\times \frac{\sin {30}^0}{\sin {56}^0}=24.12m\end{array}$

Height of tree is $24.12m$

Conclusion:

Thus, the height of tree is $24.12m$