Question

In triangle ABC ∠A=120°. AB=AC= 10 centimetres. What is the length of BC?

• A. 5√3
• B. 10√3
• C. 10+√3
• D. 5+√3

Answer 1

Answer:

B. 10√3

In triangle ABCABC, we are given:

• ∠A=120

• AB=AC = 10 cm (i.e., triangle ABC is isosceles with AB = AC).

We need to find the length of BC.

Step 1: Use the Law of Cosines.

The Law of Cosines states that in any triangle:

BC²=AB²+AC²−2×AB×AC×cos⁡(∠A)

Substitute the known values:

• AB=AC=10 cm,

• ∠A=120⁰,

• cos⁡(120⁰)= −½

So, we have:

BC²=10²+10²−2×10×10×(−½)

BC²=100+100+100=300

Thus,

BC=√300=10√3 cm.

Conclusion:

The length of BC is 10√3cm, which is approximately 17.32cm

OR

Let P be the midpoint of BC

AP = 10 × sin60

= 10 × √3/2

= 10√3/2

= 5√3

Similarly

PC = 5√3

AC = 5√3 + 5√3

= 10√3