Determine the height of a mountain if the elevation of its top at an unknowndistance from the baseÂ is 25 o 10' and at a distance of 5km further off from the mountain, along the same line, the angleofÂ elevation is 15 o 20'. Give the answer in km correct to2 decimals.

Question

Determine the height of a mountain if the elevation of its top at an unknowndistance from the baseÂ is 25 o 10' and at a distance of 5km further off from the mountain, along the same line, the angleofÂ elevation is 15 o 20'. Give the answer in km correct to2 decimals.

Philoid · Accepted Answer

Given:

Distance further away from the mountain, d = 5 km

Angle of elevation from 1 ^st point, θ = 25° 10’

Angle of elevation from the 2 ^nd point, ϕ = 15 ° 20 ’

To find: Height of the mountain

Solution:

In the figure, Let A be the mountain top. C and D are points of observation.

In right angled Δ ABC,

tan 25° 10' = AB / BC

BC tan 25° 10’ = AB
BC = AB / tan (25° 10’)

BC = AB / 0.4699

In right angled Δ ABD,

tan 15° 20' = AB / BD

tan 15° 20' = AB (BC + 5) ……………………………… [BD = BC + 5]

0.2742 = AB / (BC + 5)

Substituting BC = AB / 0.4699

= 0.2742

0.4699 AB = 0.2742(AB + 2.3495)

0.4699 AB - 0.2742 AB = 0.644

0.1957 AB = 0.644

AB = 0.644 / 0.1957

= 3.29 km

∴ The height of a mountain is 3.29 km.

Determine the height of a mountain if the elevation of its top at an unknowndistance from the baseÂ is 25 o10' and at a distance of 5km further off from the mountain, along the same line, the angleofÂ elevation is 15 o20'. Give the answer in km correct to2 decimals.

Determine the height of a mountain if the elevation of its top at an unknowndistance from the baseÂ is 25^o10' and at a distance of 5km further off from the mountain, along the same line, the angleofÂ elevation is 15^o20'. Give the answer in km correct to2 decimals.