The angle of elevation of the top of a tower at a point on the horizontal line through the foot of the tower is 45°.After walking a distance of 80m towards the foot of the tower along the same horizontal line, the angle of elevation of the top of the tower changes at 60°.Find the height of the tower.
Answers
Given :- The angle of elevation of the top of a tower at a point on the horizontal line through the foot of the tower is 45°.After walking a distance of 80m towards the foot of the tower along the same horizontal line, the angle of elevation of the top of the tower changes at 60°.
To Find :- Find the height of the tower. ?
Answer :-
Let us assume that, the height of the tower is h m and the length of horizontal line is b m .
so,
→ tan 45° = h / b
→ h = b .
now, after walking 80m towards foot of the tower ,
→ Line left = (b - 80)m .
then,
→ tan 60° = h / (b - 80)
→ √3 = h / (h - 80)
→ √3h - 80√3 = h
→ √3h - h = 80√3
→ h = 80√3/(√3 - 1)
→ h = (80*1.73) /(1.73 - 1)
→ h = (80 * 1.73) / 0.73
→ h ≈ 189.6 m (Ans.)
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