Question

angle of depression of the bottom and top of a 10 m tall building from the top of a tower are 45º and 30º respectively. Prove that the height of the tower and the distance between the tower and the building are equal. Also, find their values.​

Answer 1

Step-by-step explanation:

Correct option is C) Let the height of the tower be H we can see that, BCDE is a rectangle so, BE=CD=10& BC=DE Also, we can see that, H=AC+CD⇒H=AC+10⇒AC=H−10 Now, in △ADE tan45o=DEAD⇒1=DEAD⇒AD=DE⇒DE=H BC=DE=H Now, in △ABC tan30 o = BC AC ⇒ 3 1 = H H−10 ⇒H= 3 H−10 3 ⇒10 3 =( 3 −1)H ⇒H= 3 −1 10 3 = ( 3 −1)( 3 +1) 10 3 ∗( 3 +1) =5 3 ( 3 +1)=15

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