Answer:
x = 32.7
Step-by-step explanation:
High school geometry can throw you off really hard. One year, you're learning about transformations, then the next you have to write PROOFS. But it's alright because we can take this problem.
We can observe that we have a right triangle. Sadly, we can't use the Pythagorean Theorem to solve for x because we're not given the length of the hypothenuse. But, we could use one other thing: trigonometric functions.
Trigonometric functions are functions that relate sides of a triangle to an angle θ on that triangle. The three main trigonometric functions are sine, cosine, and tangent, and all three are defined as follows:
Sine θ = Opposite / Hypothenuse
Cosine θ = Adjacent / Hypothenuse
Tangent θ = Opposite / Adjacent
You can memorize this by remembering the phrase: SOHCAHTOA. Note that an angle is opposite to a side if it's directly opposite from it and is adjacent to a side if the side is not the opposite side nor the hypothenuse, the longest side on a right triangle.
So, how do we use trigonometry to solve the problem.
First, let's find our θ, the angle of our triangle. We can see that we have an angle of 61 degrees, so we can say that θ is 61 degrees. We can also say that θ is opposite to the side of 59 and adjacent to the side of x. We can put this into an equation and solve for x.
IMPORTANT: IF YOU ARE USING DEGREES, SET YOUR CALCULATOR TO DEGREES AND NOT RADIANS WHEN DOING CALCULATIONS.
tan θ = opposite / adjacent
tan(61) = 59 / x
x = 59 / tan(61)
x = 32.7
Therefore, we can say that x = 32.7.
