Question

The elevation of the summit of a mountain from its foot is 45°. After ascending 2 km towards the mountain upon an incline of 30°,the elevation changes to 60°. What is the approximate height of the mountain?​

Answer 1

Answer:

Let A be the foot and B be the summit of the mountain OB at height h.

In △AOB,

tan 45∘ = OB / OA

1= OB/OA

OA = h

In △ACP,

sin 30° = PC/AP

1/2 = PC /2

PC = 1

Also 30° = AC/ AP

√3/2 = AC /2

AC = √3

Now,

h=OA

h=AC+OC

h=OC+ √3

OC=h−√3

PD=h−√3

Now, in △PDB,

tan 60°= BD/PD

√3 = h-1 / h-√3

√3 h−3=h−1

h = 2/√3-1

h= √3 +1

h≈2.732 km

Hence, the height of the mountain is 2.732 km.

Answer 2

Step-by-step explanation:

the height of the mountain is 2.732

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