AB = 14cm
We find 16 if we do not see the degree sign, say if we used 16 as the radius, but the answer is 14cm or 14 units.
32 represents the top angle or the diameter
If it is angle then we can come back to it.
90-32 = 58
As all angles may be = 90, 32 and 58
If the measure is the diameter which is more likely
Then 32 is also represented as the hypotenuse and 16 is representing the radius as it is 1/2 and we can see an equilateral triangle too from the center diameter to point B.
Where all sides must be equal.
So 16 cm must be our answer.
We can check what the angles are now.
They are 30 and 60, 90 and the other side of the triangle would be 27.7cm
As 32² - 16² =
√ 1024 - √ 256 = √ 768 = 27.7cm
AB = 16cm
But then we notice the degree sign and its just as well as we can easily work it out for real now with the above workings.
If radius 16 is equilateral triangle sides all 16 = top angle = 30
If radius 14 is equilateral triangle sides all 14 - top angle = 32
This is because the sides go up the same value when the angles increase. Angle 32 must also add up to 180 so the first try for angles was correct 180-32-58 = 90
We can now prove the other sides are 8.75² and 16.50² as the squares of these numbers add up to the product of 14² and we then see 196 is that product, so in Pythagoras we square root that √196 with the sign =14 and this is making 14 the answer.
a² + b² = c²
try the above but rearrange
c² -a² = b² for finding base
c²- b² = a for finding side (that is once we have 2 sides of course)
We just happen to remember 32 angle on a right angle has a 14unit = there is no pattern its more about the 90, 32 and 58 just cannot be without a 14 unit side.
But we can use a² or b² for any side or any base really
As long as we keep c² as the hypotenuse for right angles.
We had found the base as we had to use trigonometry if we didn't know about 32,58,90 degree = 8.75 unit and 14 unit to try remember 16.50 in those degree triangles would be last priority as it represents c and c is easiest to find in trigonometry the sides are most important as we find addition most easiest too.
Hope this helps.
