# trigonometry(opt math)

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From the roof and basement of a house 20m high,the angle of elevation of the top of a tower are 45 and 60 degres respectively. Find the height of the tower.
(Ans=81.97m)

• trigonometry(opt math) -

h = height of tower

d = distance to tower

h / d = tan(60º)

(h - 20) / d = tan(45º)

h / (h - 20) = tan(60º) / tan(45º)

h = tan(60º) * (h - 20)

h [tan(60º) - 1] = 20 * tan(60º)

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