Question

How to find the following pronumeral in the diagrams below?

Answer 1

I will do (a) and leave the rest as an exercise. There are two circle properties you should be aware of:

1) The angle formed between a radius and a tangent (line touching the circle at one and only one point) is always 90˚ .

2) If two chords are formed that link together and both chords link to the same diameter (one at either end), the angle opposite the centre is 90˚ (this property is applicable for (c)).

Here is how we would approach (a). Knowing that the triangle is right, we can use SOHCAHTOA.

`tantheta = "opposite"/"adjacent" = 15/5 = 3`

`theta= arctan(3) = 72˚`

Hopefully this helps!