Originally Posted by

**David Green** I have a triangle, two side lengths are known and one angle, then a right angle triangle is added to the triangle, please see diagram below.

I am asked to find the length of AD, I used the sine rule to find it.

I am asked to calculate the angle ABD, I used sin theta = opp / hyp.

I am asked to calculate angle ABC, I subtracted 180 - theta = angle ABC

I am asked to find the length DC, given I worked out AD and knew AC I figured Pythagoras could be used.

This is where the problems begin!

I was asked to find the length DB, now I have calculated the length AD and DC, and the hypotenue is known at 8cm, however after using Pythagoras to work the length out DB which was calculated at 1.23cm, I found that DC - DB = 2.25cm and not 1.23cm using Pythagoras,

So my question is;

Looking at the diagram I have a triangle with a right angle triangle added to it, there is two hypotenuse 3 and 8, but I think triangle ADB cannot have pythagoras used to solve the lengths of the sides?

Please advise if you can.

Thanks

David