Question

from the top of the hill the angle of depression of two consecutive kilometre stones due to East are found 45 , 30 degree find the height of Hill?​

Answer 1

solution...

now..

CD=1km(two consecutive kilometre stones)

let the height of the hill is(AB) =h

now...

tan45°=AB/AC

=>1=h/AC

=>h=AC

Now....

tan 30°=AB/AD

=>1/√3=h/(AC+CD)

=>1/√3=h/(h+1)

=>√3 h=h+1

=>h(√3-1)=1

=>h=1/(√3-1)

$= > h = \frac{( \sqrt{3} + 1) }{( \sqrt{3} - 1)( \sqrt{3} + 1) } = \frac{ \sqrt{3} + 1}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1.732 + 1}{2} = 1.366 \: \: km$