Answer:
x ~= 61.0°
Explanation:
This is a trig question. The marked angle is unknown so we will use an inverse trig function to find a missing angle. On your calculator you may need to use the 2nd button or shift to get not just "cos" but the inverse cos. It might look like cos with a -1 exponent or "arccos" or "acos"
So the triangle is a right triangle. The angle is next to one of the given sides. "Next to" is called "adjacent" these mean the same thing. One side is adjacent to the angle. The other given side is the hypotenuse.
The trig function that puts together Adjacent and Hypotenuse is cosine.
cos (angle) = adj/hyp
We know the two sides. Fill them in.
cos (angle) = 31/64
We are looking for the angle.
cos x = 31/64
Use the inverse cos to find the angle.
cos^-1 (31/64) = x
This is a calculator activity. Unless your teacher has given you tables of values (this is how it was done before calculators) you have to use a calculator.
x = 61.0284677763
round to the nearest tenth.
x ~= 61.0