For the sake of easy checking, what answers did you get when you calculated the length of AD, the angle ABD, angle ABC, and the length DC?
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.
I would use the fact that
Which gives which is what you have (which is correct).
I agree with all solutions so far. I also agree that
going by what we have so far.
We can confirm that using the cosine rule:
which comes out at
, as we'd expect.
so using pythagoras then resulting in a answer of 1.23 against your 1.22 is this completely wrong or a rounding error?