Question

In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°?
A) 12√3 cm B) 6 cm C) 12 cm D) 3√3 cm

Answer 1

QUESTION:

In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°?

A) 12√3 cm B) 6 cm C) 12 cm D) 3√3 cm

ANSWER:

Refer the attachment for the figure;

Concept of the question :

If we let <c = 60° then the side opposite to that angle is AB.

and

If we let angle B = 90° then the side opposite to that angle is AC.

TO FIND = length of AC

Now, this is a right angle triangle we use the trigonometry rule.

$\tan( \alpha ) = \frac{perpendicular}{base}$

so,

According to figure;

$\tan(60) = \frac{ab}{bc}$

$\sqrt{3} = \frac{6 \sqrt{3} }{bc} \\ bc = 6cm$

now;

$\cos( \alpha ) = \frac{base}{hypotenuse}$

ACCORDING TO figure

$\cos(60) = \frac{bc}{ac}$

$\frac{1}{2} = \frac{6cm}{ac} \\ ac = 12cm$

FINAL ANSWER :

the length of the side opposite to angle 90 is 12 cm

Your answer is option c.