Points A,B and C are taken in the ascending order lie on a straight line inclined at an angle `theta`  to the horizontal. AB = x and D is the point vertically above at height h from point C. CD...

Points A,B and C are taken in the ascending order lie on a straight line inclined at an angle `theta`  to the horizontal. AB = x and D is the point vertically above at height h from point C. CD subtends angles `alpha`  and `beta`  at A and B respectively.

`h = (xsinalphasinbeta)/(sin(beta-alpha)costheta)`

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

The situation is attached in the image.

According to the description given and using the image;

`angleDAB = alpha`

`angleDBC = beta`

`angleCAE = theta`

Applying sine law for triangle ACD

Applying sine law for triangle ABD

`h = (xsinbeta)/(sin(beta-alpha))xx(sinalpha)/(costheta)`

So the required answer is proved.

`h = (xsinbetasinalpha)/(sin(beta-alpha)costheta)`

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