I’m finally trying to understand trigonometry and came across this random quiz question:
As you can see, I got this wrong. I’m having a hard time understanding why. Based on what I know we have:
- A hypotenuse of 9
- An adjacent of 5
So, we use cosine since we have the adjacent and hypotenuse.
cos(theta) = A/H
which would be
cos(theta) = 0.55
So, theta would be:
acos(0.55)
And to transform the radians in to degrees:
acos(0.55) * (180 / PI)
However, this gives me 56.63 which isn’t close to any of the options there.
>Solution :
You cannot consider 5 or 9 as the adjacent side since it is not a right angle triangle, but an isosceles triangle. Based on the markings, the unlabelled side also has length 5cm.
Given the lengths of 3 sides, we can find any angle with the Cosine Law. Here, we get:
5^2 = 9^5 + 5^2 - 2(9)(5)cos(x)
cos(x) = (9^2 + 5^2 - 5^2) / (2*9*5)
cos(x) = 9/10
x = arccos(0.9) ≈ 25.8°