What is the height of a mountain when the distance between its angles of elevation which are 16.6 degrees and 22.3 degrees on level ground is 500 meters?

What is the height of a mountain when the distance between its angles of elevation which are 16.6 degrees and 22.3 degrees on level ground is 500 meters?
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This can be solved using the Tangent trigonometric ratio.The larger angle of elevation is the closer angle.Let the horizontal distance from this point to the peak of themountain be d metres; then:height = d × tan 22.3°The second point is a further 500 m from the peak with anelevation of 16.6°; this gives:height = (500 + d) × tan 16.6°As the height is the same at both measurements, these two valuesmust be equal:→ d × tan 22.3° = (500 + d) × tan 16.6°→ d × (tan 22.3° - tan 16.6°) = 500 × tan 16.6°→ d = 500 × tan 16.6° / (tan 22.3° - tan 16.6°)→ height = d × tan 22.3°= 500 × tan 16.6° / (tan 22.3° - tan 16.6°) × tan 22.3°≈ 546 m(Generally mountains are more than 600 m, so this is more of ahill.)
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