Question

At the foot of a mountain, the elevation of its summit is 45 degree. After ascending 1 km towards the mountain up an inclination of 30 degree the elevation changes to 60 degree. Find the height of the mountain.

Answer 1

Answer:

the height of the mountain is 1.366 km

Step-by-step explanation:

Please see the picture for given problem description.

In the figure, AB represents the mountain of height h, say. In ΔFCE,

Sin(30) = CE/FC  

It is given that FC = 1000 meters

½ = CE/1000

CE = 500 meters

Cos(30) = FE/FC

√(3)/2 = FE/1000

OE = 500√(3)

In AFB, tan(45) = AF/AB

FA = AB

CD = EA = FA - FE = h - 500√(3)

BD = AB - AD = AB - CE = h - 500

In ΔBCD,

tan(60) = BD/CD

√(3) = (h - 500)/(h - 500*√(3))

Simplifying we get  

h(√(3) - 1) = 1000

h = 1000/(√(3) - 1)

h = 1366 meters

Thus, the height of the mountain is 1.366 km

Answer 2

Step-by-step explanation:

i hope this will help you