Question

from the top of a 7 high building the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 45 determine the height of the tower ​

Answer 1

so so in the above picture is your figure and according to this figure your answer will be as follows -

Let AB be the building of height 7 m and EC be the height of tower. A is the point from where elevation of tower is 60° and the angle of depression of its foot is 45° EC = DE + CD also, CD = AB = 7 m. and BC = AD A/q, In right ΔABC, tan 45° = AB/BC ⇒ 1= 7/BC ⇒ BC = 7 m = AD also, In right ΔADE, tan 60° = DE/AD ⇒ √3 = DE/7 ⇒ DE = 7√3 m Height of the tower = EC = DE + CD = (7√3 + 7) m = 7(√3+1)

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