Answer:
angle = 50.8° (to the nearest tenth of a degree)
Step-by-step explanation:
In a right triangle:
We have been given the measures of the shorter leg and the hypotenuse, so the angle between them is the larger acute angle (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: [tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
If [tex]\theta[/tex] is the angle, then the short leg is the "adjacent" side to the angle and the "hypotenuse" is the hypotenuse.
Substituting the given values:
[tex]cos(\theta)=\frac{3\sqrt{6} }{3\sqrt{15} }[/tex]
⇒ [tex]\theta=arccos(\frac{3\sqrt{6} }{3\sqrt{15} })=50.76847952..[/tex]
Therefore, the angle = 50.8° (to the nearest tenth of a degree)
