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One leg of a right triangle measures 6 inches. The remaining leg measures 6√3 inches. What is the measure of the angle opposite the leg that is 6 inches long?

Respuesta :

30°
Here's why:
Using the well-known Pythagorian theorem we can reckon how long the hypotenuse is:
c^2=6^2+36*3 -> c=12
Knowing that sin(a)=a/c=6/12=0.5 the measure of the angle in degrees is 30°
Hope could help :)
isyllus

Answer:

30°

Step-by-step explanation:

One leg of a right triangle measures 6 inches.

Leg 1 (Opposite) = 6

The other leg measure [tex]6\sqrt{3}[/tex] inches.

Leg 2 (Base ) = [tex]6\sqrt{3}[/tex]

Let the measure of angle opposite of the leg 6 inches be Ф

Using trigonometry identity

[tex]\tan\theta=\dfrac{\text{Opposite}}{\text{Base}}[/tex]

[tex]\tan\theta=\dfrac{6}{6\sqrt{3}}[/tex]

Cancel 6 from top and bottom

[tex]\tan\theta=\dfrac{1}{\sqrt{3}}[/tex]

[tex]\theta=\tan^{-1}(\frac{1}{\sqrt3})[/tex]

[tex]\theta=30^\circ[/tex]

Hence, The measure of opposite angle of leg 6 inches is 30°

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