More on the relationship between sides and angles in similar triangles
In triangle ABC, let’s consider the angle 53.1. When we are talking about that angle, the opposite is side BC which is 12 units long. The hypotenuse has length of 15.
If we call the length of the opposite side O and the length of the hypotenuse H then
O ÷ H
= 12 ÷ 15
= 0.8
Let’s consider the similar triangle DEF.
For this triangle
O ÷ H
= 8 ÷ 10
= 0.8
The value of O ÷ H is the same for both triangles. It turns out that for any right angled triangle with a value of O ÷ H = 0.8 the angle is always 53.1.
This means for a right angled triangle, with an angle of 53.1, if we know the length of the hypotenuse, we can work out the length of the opposite. Also, if we know the length of the opposite, we can work out the length of the hypotenuse.
If we had a right angled triangle with the following information, we’d be able to work out the length of the side opposite the angle of 53.1°.
We know that for an angle of 53.1 degrees
O ÷ H = 0.8
O ÷ 20 = 0.8
O = 0.8 * 20
= 16
