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.

Show that

`d = (xsin(alpha+theta)sinbeta)/(sin(beta-alpha))`

where d is the height of D above level of A.

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The notation for this question is same as the following question.

http://www.enotes.com/homework-help/points-b-c-taken-ascending-order-lie-straight-line-442230#answer-624263

According to the new data d = DE

By the image we can say that;

`DE = d = ADsin(alpha+theta)`

In the previous question we have obtained that;

`AD = (xsinbeta)/(sin(beta-alpha))`

`d = (xsinbeta)/(sin(beta-alpha))xxsin(alpha+theta)`

`d = (xsinbetaxxsin(alpha+theta))/(sin(beta-alpha))`

*So the required answer is proved.*

`d = (xsinbetaxxsin(alpha+theta))/(sin(beta-alpha))`

**Sources:**

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