Question

The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances $49m$ and $36m$ are ${43}^{\circ }$ and ${47}^{\circ }$ respectively. What is the height of the tower?

• A. $40m$
• B. $42m$
• C. $45m$
• D. $47m$

Answer 1

The correct option is B

$42m$

Step 1: Consider the following figure that represents the problem

Suppose the height of the tower is $h$.

Step 2: Obtain the equation for the height

From the figure, it is clear that,

$\tan 47°=\frac{h}{36}······\left(1\right)$ and $\tan 43°=\frac{h}{49}·······\left(2\right)$

$\tan 43°$ can also be written as $\tan \left(90-47\right)°$. So,

$$\begin{gathered} \tan \left(90-47\right)°=\frac{h}{49} \\ \mathrm{co}t47°=\frac{h}{49}·····\left(3\right) \end{gathered}$$

Step 3: Obtain the value of height

Multiply, the equation $\left(1\right)$ and $\left(3\right)$,

$\begin{array}{rcl}\tan 47°\times \mathrm{co}t47°& =& \frac{h}{49}\times \frac{h}{36}\\ 49\times 36& =& h^2\\ 42& =& h\\ h& =& 42m\end{array}$

Hence, option (B) is the correct answer.