Chapter 9, Problem 12CST

a.

To determine

To find the value of $a$ to the nearest foot.

Answer to Problem 12CST

The value of $a$ in nearest foot equal to $214.45ft$

Explanation of Solution

Given: The two buildings are $100ft$ away each other.

Calculation:

The value of $a$ is obtained by,

  $\begin{array}{l}\mathrm{Tan}{65}^0=\frac{a}{100}\\ \Rightarrow a=(100)\mathrm{Tan}{65}^0\\ \Rightarrow a=(100)(2.14)\\ \Rightarrow a=214.45\approx 214ft\end{array}$

Hence, the value of $a$ is $214.45ft$ .

b.

To determine

To find the value of $b$ to the nearest foot.

Answer to Problem 12CST

The value of $b$ in nearest foot equal to $143ft$

Explanation of Solution

Given: The two buildings are $100ft$ away each other.

Calculation:

The value of $b$ is obtained by,

  $\begin{array}{l}\mathrm{Tan}{55}^0=\frac{b}{100}\\ \Rightarrow b=(100)\mathrm{Tan}{55}^0\\ \Rightarrow b=(100)(1.428)\\ \Rightarrow a=142.81\approx 143ft\end{array}$

Hence, the value of $b$ is $143ft$ .

c.

To determine

To find the height of the tallest building.

Answer to Problem 12CST

The height of the tallest building $=a+b=214+143=357ft$

Explanation of Solution

Given: The height of the building is obtained by add $a\text{ and b}$ .

Calculation:

The height of the tallest building $=a+b=214+143=357ft$

d.

To determine

To explain how to use trigonometric ratios in part $a\text{ and b}$ .

Answer to Problem 12CST

The value of $a$ and $b$ , it is better to write as, $\mathrm{Tan}\theta =\frac{opposite}{adjacent}$

Explanation of Solution

Given:

In the given figure the length between two buildings is given as $100ft$ and the angle also mentioned as ${65}^0$ to find the value of $a$ and $b$ in above parts.

Calculation:

To find the value of $a$ and $b$ , it is better to write as, $\mathrm{Tan}\theta =\frac{opposite}{adjacent}$