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Neporo4naja [7]
2 years ago
15

PLEASE HELP!!!!!!!!!!!!!!

Mathematics
1 answer:
Alex17521 [72]2 years ago
3 0

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: cos(\theta)=\frac{adjacent}{hypotenuse}

If \theta is the angle, then the short leg is the "adjacent" side to the angle and the "hypotenuse" is the hypotenuse.

Substituting the given values:

cos(\theta)=\frac{3\sqrt{6} }{3\sqrt{15} }

⇒ \theta=arccos(\frac{3\sqrt{6} }{3\sqrt{15} })=50.76847952..

Therefore, the angle = 50.8° (to the nearest tenth of a degree)

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