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The hypotenuse of a right triangle measures 3√15 centimeters and its shorter leg
measures 3√6 centimeters. What is the measure of the larger acute angle of the triangle?
Round your answer to the nearest tenth of a degree.

Sagot :

Semsee45idn

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 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)

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