Answer:
66.423 degrees
Step-by-step explanation:
The diagram is a right-angled triangle. It has two known sides and one known interior angle which is 90 degrees. The side opposite to the 90 degrees is called the Hypotenuse. it is also the longest side.
To find an angle, you need to know two sides. Per the angle at Y or angle XYZ, XY is adjacent. Using the adjacent XY and Hypotenuse YZ, we can write an expression using the trigonometric ratio called Cosine.
That's, Cos XYZ= 6/15
Angle XYZ=Cosine Inverse of 6/15
Angle XYZ=66.42. (2 dp)
