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# How do you work out the remaining side of a right angled triangle using theta and one side?

Wiki User

2016-05-15 18:59:12

Suppose triangle ABC is right angled at C. Suppose you are given that the angle at B is theta. Then

if you know the length of AB (the hypotenuse), then

BC = AB*cos(theta) and

AC = AB*sin(theta)

if you know the length of BC, then

AB = BC/cos(theta) and

AC = BC*tan(theta)

if you know the length of AC, then

AB= AC/sin(theta) and

BC = AC/tan(theta)

Wiki User

2016-05-16 15:31:57
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Wiki User

2016-07-05 18:36:31

sin theta = opposite/hypotenuse

So if you know the length of the shorter side adjacent to theta,...
opposite = adjacent * tan theta
hypotenuse = adjacent / cos theta

If you know the length of the side opposite theta,...
adjacent = opposite / tan theta
hypotenuse = opposite / sin theta

If you know the length of the hypotenuse,...
opposite = hypotenuse * sin theta
adjacent = hypotenuse * cos theta