Question

The angles of elevation of the top of a hill at the city centres of two towns on either side of the hill are observed to be 45 degree and 60 degree. If the distance uphill from the first city centre is 12 km, then find in km, the distance uphill from the other city centre.

Answer 1

i hope this will help u.....

Answer 2

The distance uphill from the other city Centre is (12/√3).

Given:

the angle of elevations from the two towns are= 45 degree and 60 degree

distance of uphill from the first city Centre = 12 km

solution:

draw the diagram as per the question

AB= top hill

∠ABD= 45c

∠ACD=60°

BD= 12 km

let the distance of  the uphill to other city is x.

solving

in

triangle ABD

tan 45° = AD/BD

⇒ 1= AD/12

⇒ AD= 12

Taking the triangle

ADC

tan 60°= AB/DC

⇒12/x =  √3

⇒x= 12/√3

so distance from uphill from other city is 12/√3.

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