If I have a triangle of 90, 14 and 76 degrees and I am asked to find the opposite / adjacent ratio of 76 degrees without using the tangent of it with the calculator, what can be the method? Thank you.

Question

I have as a reference this triangle a triangle of 90,11 and 79 degrees where the opposite / adjacent ratio is 1/5 (6/30)

Answer 1

The opposite side should be length 4 or a multiple of 4, and the adjacent side should be the multiplier itself. For example, 4/1, 8/2, 12/3, 16/4, etc. All of these give a tangent of about 4 for the 76 degree angle. It follows that the tangent of 14 degrees must be ¼ (approx).

Graphically, draw a right-angled triangle by marking 4 on the y-axis and 1 on the x-axis, joining these points together and also joining each point to the origin. If you measure the angles you should get 76° and 14°.