Question

In a triangle ABC right angled at B, AB = 12cm and <CAB=60°. Determine the lengths of the other two sides.​

Answer 1

Answer:

bc=12√3

ac=24

Step-by-step explanation:

Answer 2

The lengths of the other two sides are 12√3 cm and 24 cm.

Given:

ΔABC is right-angled at B,  AB = 12cm and ∠CAB=60°.

To Find:

The length of the other two sides.

Solution:

We have been given that ΔABC is right-angled at B and ∠CAB=60°.

AB, which essentially forms the height of ΔABC, is 12 cm long.

Here we will find out trigonometric ratios of angle A and find out the lengths of the remaining two sides.

In ΔABC,

AC is the hypotenuse.

AB = 12 cm is the side adjacent to ∠A.

BC is the side opposite to ∠A.

We need to find out the lengths of AC and BC.

Now, in ΔABC

cos A = $\frac{Adjacent &\ side}{Hypotenuse}$ = $\frac{AB}{AC}$ = $\frac{12}{AC}$

⇒ cos 60° = $\frac{12}{AC}$

⇒ $\frac{1}{2}$ = $\frac{12}{AC}$

⇒ AC = 24 cm.

sin A = $\frac{Opposite &\ side}{Hypotenuse}$ = $\frac{BC}{AC}$

⇒ sin 60° = $\frac{BC}{24}$

⇒ $\frac{\sqrt{3} }{2}$ = $\frac{BC}{24}$

⇒ BC = 12√3 cm.

Hence the lengths of the other two sides are 12√3 cm and 24 cm.

#SPJ3