As you may already know, you can only calculate the relative lengths and NOT the actual side lengths of a triangle when you are given all 3 angles.
As an example, let's take triangle ABC in which angle A = 50°, angle B = 60° and angle C = 70°.
For calculating the third side (BC), we need to use two Pythagorean Theorem equations.
side x² = 1.1547² - 1² = .33333 side x = 0.57735
Let's "neaten up" those numbers just a bit, by multiplying each of those sides by the reiprocal of the shortest side.
By doing this we get:
To check if your calculations are correct, go to this calculator, select "3 sides", enter 1, 1.1305 and 1.2266 then click "calculate".
Easier Method
![]() Look up the sine values for each of the angles: Sine 35° = 0.57358 Sine 50° = 0.76604 Sine 95° = 0.99619 And that's it!
Granted we could "neaten up" the numbers by multiplying them by the reciprocal of the smallest side 1 ÷ .57358 = 1.743436
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