Question

In the right angled triangle ABC, angle C=90 degree and angle B =60 degree.If AC=6 cm,find the lengths of the sides BC and AB

Answer 1

given:
   c=90
b=60
cos 60=BC/AB
⇒1/2=BC/AB
sin 60=AC/AB
⇒√3/2=6/AB
AB=4√3
BC=2√3

Answer 2

Given - Angles

Find - Side BC and AB

Solution - As per the given information, side AC is assumed to be perpendicular. Therefore, the side BC will be base of right angle triangle. Subsequently, the side AB will be hypotenuse.

$\tan(60) = \frac{AC}{BC}$

$BC = \frac{AC}{ \tan(60) }$

Keep the values in formula

$\tan(60) = \sqrt{3}$

Performing division

$BC = \frac{6}{ \sqrt{3} }$

$BC = 3.5 \: cm$

$\sin(60) = \frac{AC}{AB}$

$AB = \frac{AC}{ \sin(60) }$

Keep the values in formula

$AB = \frac{6}{( \sqrt{3} \div 2)}$

Performing multiplication and division

$AB = \frac{6 \times 2}{ \sqrt{3} }$

$AB= \frac{12}{ \sqrt{3} }$

$AB = 7 \: cm$

So, the angles BC and AB are 3.5 and 7 cm respectively.