Question

Example 4. Determine the height of a mountain, if
the elevation of its top at an unknown distance from
the base is 30° and at a distance 10 km further off from
the mountain, along the same line, the angle of
elevation is 15º. (Take tan 15° = 0.27)​

Answer 1

Given :-

Angle of elevation from an unknown distance = 30°

Angle of elevation 10 km away from the unknown distance = 15º

To Find :-

Height of the mountain.

Solution :-

Let us consider 'h' as the height.

$\sf tan \ 15^{o}=\dfrac{h}{BD}$

Given that, tan 15° = 0.27

$\implies \sf 0.27=\dfrac{h}{BD}$

$\sf h=0.27(x+10)$

$\longrightarrow \sf 0.27x+2.7=h \qquad ...(1)$

In ΔABC,

$\sf tan \ 30^{o}=\dfrac{h}{x}$

$\sf h=\dfrac{x}{\sqrt{3} }$

$\sf \longrightarrow h\sqrt{3} =x \qquad ...(2)$

From equation (1),

$\sf0.27(h\sqrt{3})+2.7=h$

$\sf h(1-0.27 \times \sqrt{3} )=2.7$

$\sf h=\dfrac{2.7}{1-0.27 \times \sqrt{3} }$

$\sf h=5$

Therefore, the mountain is 5 km high.

Answer 2

Answer:

5km

Step-by-step explanation:

please refer to the attachment.

Hope it helps..