Chapter 9.8, Problem 4E

1.

To determine

Tofind:Equation for height of tower

Answer to Problem 4E

  $h=\left(\sin {70}^{\circ }\right)225$

Explanation of Solution

Given information:

Length of support wire $=225\text{ ft}$

Angle between wire and ground $={70}^{\circ }$

Height of tower $=h$

Concept Used:

In a right-angled triangle ABC, sine for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of hypotenuse and cosine of acute angle $\angle A$ is the ratio of length of side adjacent to angle $\angle A$ to the length of hypotenuse.

Calculation:

Basis definition we can say-

  $\begin{array}{l}\sin {70}^{\circ }=\frac{Opposite}{Hypotenuse}\\ \Rightarrow \sin {70}^{\circ }=\frac{h}{225}\\ \Rightarrow h=\left(\sin {70}^{\circ }\right)225\end{array}$

2.

To determine

Tocalculate:The height of the tower

Answer to Problem 4E

  $h\approx 211$

Explanation of Solution

Given information:

  $h=\left(\sin {70}^{\circ }\right)225$

Calculation:

We can calculate the value of tan using calculator with following steps-

• Keep the calculator on degree mode
• After selecting tan, angle must be written inside parenthesis.
• If the decimal is non-terminating, round the value to 4 decimals

By using above steps, we can calculate given value as-

  $\begin{array}{l}h=\left(\sin {70}^{\circ }\right)225\\ h= \left(0.9396\right)225\\ h= 211.4308\\ h\approx 211\end{array}$