Answer to Question #174575 in Algebra for Surendra Singh

Question

The angle of elevation from ground to the top of building and to the top of chimney which is at the top of building are x0 and 450 respectively. The height of building is h. What is height of chimney in meters?

Answer 1

Let the height of the building AH = a, the height of the chimney HB = b.

Then AB = a + b. According to the task $\angle{ACB}$ = x, $\angle{ACH}$ = 45$\degree$.

1) From triangle ABC :

$\tan{x}$ = $\frac{AB}{AC}$

AB = AC $\tan{x}$

AC = $\frac{AB}{\tan{x}}$ = $\frac{a+b}{\tan{x}}$ .

2) From triangle ABH :

$\tan{45\degree}$ = $\frac{AH}{AC}$

AH = AC $\tan{45\degree}$

AH = AC

AC = AH = a.

3) From 1) and 2) :

$\frac{a+b}{\tan{x}}$ = a

a + b = a $\tan{x}$

b = a $\tan{x}$ - a.

Hence the height of the chimney is (a $\tan{x}$ - a).