Question

The angles of depression of the top and bottom of a 8m tall building from
the top of a multi storied building are 30' and 45°, respectively. Find the
height of the multi storied building.
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Answer 1

Step-by-step explanation:

Abdul Kalam, in full Avul Pakir Jainulabdeen Abdul Kalam, (born October 15, 1931, Rameswaram, India—died July 27, 2015, Shillong), Indian scientist and politician who played a leading role in the development of India's missile and nuclear weapons programs. He was president of India from 2002 to 2007.12-Feb-2021

Answer 2

let's take an triangle where

ABC is of 30° and DCB is of 45° so,

tan= perp/base

from DCB

tan45° = DB/BC

1=DB/BC

BC=DB ----i

From ACB

tan 30° = AB/CB

1/√3 = 8+DB/BC

BC√3 = 8+DN

BC=8+DB/√3 -----ii

combining i & ii

DB = 8+DB/√3

√3DB = 8+DB

√3DB -DB = 8

DB(√3 - 1) = 8

DB = 8 (√3 + 1)/(√3 -1) (√3 + 1)

DB = 8 (√3+1)/(√3)² - (1)²

DB = 8 (√3 + 1)/3-1

DB = 4 (√3+1)m

Therefore , the height of the multistoried building is 4 (√3+1)m.