trigonometry

Get theta based on known hypotenuse and adjacent


I'm finally trying to understand trigonometry and came across this random quiz question: enter image description here

As you can see, I got this wrong. I'm having a hard time understanding why. Based on what I know we have:

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°