Based on the right-angled triangle shown above, the value of x is equal to 20.7
In order to determine the value of x, we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side (13) and hypotenuse (x) of a right-angled triangle;
cos(θ) = Adj/Hyp
Where:
- Adj represent the adjacent side of a right-angled triangle.
- Hyp represent the hypotenuse of a right-angled triangle.
- θ represent the angle.
By applying the cosine trigonometric function ratio to right-angled triangle ABC, we have the following:
cos(θ) = adjacent side/hypotenuse
cos(51) = 13/x
x = 13/cos(51)
x = 13/0.62932039104983745270590245827997
x = 20.6572 ≈ 20.7
Complete Question:
Determine the value of x.