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Applications of Trigonometry
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17/06/2021 11:14 am
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From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
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17/06/2021 11:15 am
Let BC be the 20 m high building.
Height of transmission tower = AB = AC – BC
AB, Height of the tower
From figure, In right ΔBCD,
tan 45° = \(\frac{BC}{CD}\)
1 = \(\frac{20}{CD}\)
CD = 20
In right ΔACD,
tan 60° = AC/CD
√3 = \(\frac{AC}{20}\)
AC = 20√3
AB = AC – BC = (20√3 - 20)
= 20(√3 - 1)
Height of transmission tower = 20(√3 – 1) m.