Question

Two persons A and B are on the same side of a tower (T). Ifthe angles of elevation of the top of the tower as observed by A and B are 40°and 55° respectively and line /AB/ is 6m. Find the height of the tower.

Answer 1

Answer:

Height of the tower is 12.07 meter.

Step-by-step explanation:

Given:

Angle of elevation observed from A = 40°

Angle of elevation from point B = 55°

Distance from A to B = 6 m

Note :

As we move towards the tower the angle of elevation will increase.

Let the height of the tower be "h'' meter.

And the distance from B to the base of the tower be "x'' m.

Adjacent length for angle 55° is ''x'' m and adjacent length from point A that is angle 40° is "6+x" m.

And we know that:

⇒ $tan (\theta) = \frac{opposite}{adjacent}$

So arranging them in tangent angles.

⇒ $tan(55) = \frac{h}{x}$        ...equation (i)

⇒ $tan(40)=\frac{h}{x+6}$    ...equation (ii)

Dividing both the equation.

⇒ $\frac{tan(55)}{tan(40)} =\frac{h}{x}\times \frac{6+x}{h}$

⇒ $1.7=\frac{6+x}{x}$

⇒ $1.7x=6+x$

⇒ $1.7x-x=6$

⇒ $0.7x=6$

⇒ $x=\frac{6}{0.7}$

⇒ $x=8.5$ m

Now using the value of 'x' in equation (i).

⇒ $h=x\times tan(55)$  

⇒ $h=8.5(1.42)$

⇒ $h=12.07$ m

Height of the tower is 12.07 meter.

Answer 2

Answer:

12.2 meters

Step-by-step explanation:

The position of tower and the two persons has been shown in the figure below.

Let, h is the height of tower and the distance between tower and person B is x.

We can see in the figure that there are two triangles PAQ and PBQ and both are right angle triangles.

Now, In triangle PAQ, we can write

tan40⁰ = $\frac{h}{x+6}$

Thus, 0.839 = $\frac{h}{x+6}$

$0.839x + 5.034 = h$

$x = \frac{h- 5.034}{0.839}$     (equation 1)

Again, in triangle PBQ, we can write

tan55⁰ = $\frac{h}{x}$

Thus, 1.428 = $\frac{h}{x}$

$x = \frac{h}{1.428}$     (equation 2)

Now, from equation 1 and equation 2, we can write

$\frac{h-5.034}{0.839} = \frac{h}{1.428}$

$1.428h - 7.188 = 0.839h$

$0.589h=7.188$

$h=12.2$

Thus the height of the tower will be 12.2 meters.