Chapter 9.7, Problem 21E

a.

To determine

Write an expression for the height of the tree in terms of $d$ .

Answer to Problem 21E

The expression for the height of the tree is, $d+1.5mts$

Explanation of Solution

Given:

  

Calculation:

The distance from the forester to trunk of the tree $=50meters$

The distance from the forester’s eye level to the ground $=1.5meters$

The expression to find the height of the tree in terms of $d$ as follows:

  $\begin{array}{l}\mathrm{Tan}{52}^0=\frac{opposite}{adjacent}=\frac{d}{50}\\ \Rightarrow d=(50)\mathrm{Tan}{52}^0=(50)(1.28)=63.99\approx 64mts\end{array}$

Height of the tree is obtained by add value of $d$ with the distance from the forester’s eye level to ground of $1.5mt=d+1.5mts$

Hence, the expression to find the height of the tree in terms of $d$ is $d+1.5mts$

b.

To determine

To find the value of $d$ to the nearest tenth of a meter.

Answer to Problem 21E

The value of $d$ to the nearest tenth of a meter $=64mts.$

Explanation of Solution

Given:

  

Calculation:

  $\begin{array}{l}\mathrm{Tan}{52}^0=\frac{opposite}{adjacent}=\frac{d}{50}\\ \Rightarrow d=(50)\mathrm{Tan}{52}^0=(50)(1.28)=63.99\approx 64mts\end{array}$

The value of $d$ to the nearest tenth of a meter $=64mts.$

c.

To determine

To find the value of $d$ to the nearest tenth of a meter.

Answer to Problem 21E

The height of the tree $=66mts$

Explanation of Solution

Given:

  

Calculation:

The height of the tree:

Height of the tree is obtained by add value of $d$ with the distance from the forester’s eye level to ground of $1.5mt\text{ is by sustitute the value of d above expression}=d+1.5=64+1.5=65.5\approx 66mts$

Hence, the height of the tree $=66mts$