Posted by **zainab** on Tuesday, April 24, 2012 at 3:39am.

2. A person walking along a straight road observed that at two consecutive kilometre stones the angles of elevation of a hill front of him are 40o and 80o respectively. Find the height of the hill.

- arithmetic -
**Reiny**, Tuesday, April 24, 2012 at 8:15am
Make a sketch

I have A, B, and C on a horizontal line, and H as the top of the hill

Angle A = 40° and angle HBC - 80°, AB = 2 km

In triangle ABH, angle ABH = 100°

then angle AHB = 40°

which makes BH = 2 , (isosceles triangle)

(that was lucky, else I would need the sine law to find BH)

in triangle HBC (right-angled)

sin 80 = HC/2

HC = 2sin80 = 1.97 km

Wow, that is more than just a "hill"

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