Answer to Question #104460 in Trigonometry for Antoni Perez

Question

14. A fly, buzzing about the room, calculates the angle of depression of the base of an 8-foot wall is 33.7° and the angle of elevation of the top of the wall is 12.5°. Find to the nearest foot the horizontal distance the fly is from the wall.

Answer 1

Here as per question the height of wall is 8ft

so , i draw the above diagram as per question requirement

Let x be the distance of CD, then DO will be 8-x

Now, In $\Delta CDB, CD =x , BD$ is the base ,

so, $\tan \theta = \frac{CD}{BD},$

$\tan (12.5^o) = \frac{x}{BD}$

BD$= \frac{x}{.2217}$ ........................1

similarly , In $\Delta BDO$

$\tan (33.7^o)=\frac{8-x}{BD}$

BD= $\frac{8-x}{.6669}$ .......................2

From equation 1 and 2 we can write

$\frac{x}{.2217} =\frac{8-x}{.6669}$

$.6669x= 1.7736-.2217 x$

.$0.8907x=1.7736$

$x= 1.99 ft$

so just we put this value in equation 1 we get

BD = 8.98ft

so ,the dustance of fly from wall is 8.98 ft we can take it approx as 9ft