Question

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The elevation of the summit of a mountain from its foot is 45°. After
ascending 1 km towards the mountain upon an incline of 30°, the elevation
changes to 60°. The height of the mountain is?​

Answer 1

Answer

• Height of the mountain is √3+1/2

Explanation

Given

• Elevation of summit of a mountain from foot = 45
• After ascending 1 km, angle of elevation changes to 60 upon an incline of 30

To Find

• Height of mountain

Solution

● Let AB be the height of the mountain

✭ In triangle ABC

→ tan 45 = BC/AB

→ 1 = BC/AB

→ AB = BC ❲ eq(1) ❳

✭ In trangle AOD

→ sin 30 = OD/AO

→ 1/2 = OD/1

→ 2 OD = 1

→ OD = 1/2 ❲ eq(2) ❳

Also,

→ cos 30 = AD/AO

→ √3/2 = AD/1

→ 2AD = root 3

→ AD = √3/2 ❲ eq(3) ❳

✭ In triangle CED

→ tan 60 = CE/OE

→ √3 = (CB - EB)/AB - AD)

Remaining Answer has been Attached!!