Answer:
angle = 50.8° (to the nearest tenth of a degree)
Step-by-step explanation:
In a right triangle:
- The angle between the shorter leg and the hypotenuse is the larger acute angle of the triangle.
- The angle between the longer leg and the hypotenuse is the smaller acute angle of the triangle.
We have been given the measures of the <u>shorter leg</u> and the <u>hypotenuse</u>, so the angle between them is the <u>larger acute angle</u> (which we need to find).
shorter leg = 3√6 cm
hypotenuse = 3√15 cm
So to find the angle, we need to use the trig ratio:
If is the angle, then the short leg is the "adjacent" side to the angle and the "hypotenuse" is the hypotenuse.
Substituting the given values:
⇒
Therefore, the angle = 50.8° (to the nearest tenth of a degree)