The shorter leg of a 30°-60°-90° triangle is 6. What is the length of the other leg?

Mathematics

2 answers:

VLD [36.1K]3 years ago

3 0

The length of the other leg is 12, I think, but I'm not sure. Sorry if it's wrong.

Rina8888 [55]3 years ago

3 0

Answer:

$x=6\sqrt{3}$ units.

Step-by-step explanation:

It is given that shorter leg of a 30°-60°-90° triangle is 6.

In a triangle larger interior angle has larger opposite side and vice versa.

The length of shortest leg is 6 units it means it is opposite to the angle 30°.

Let the length of second leg be x.

In a right angle triangle,

$\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (30^\circ) =\dfrac{6}{x}}$

$\dfrac{1}{\sqrt{3}}=\dfrac{6}{x}}$

On cross multiplication, we get

$x=6\sqrt{3}$

Hence, the length of the other leg is $x=6\sqrt{3}$ units.

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