Question

find the value of x​

Answer 1

AnsWer :

x = 100°

Required Concept :

• Sin 20° = 2 Sin 10° . Cos 10°.

Solution :

We have, Ceva Theorem In trigonometry form.

Let angle ABP = y°.

Since, angle ABC = angle ACB = 50°

By Ceva theorem,

$\tt \dashrightarrow \sin(60) \sin(10) \sin(50 - y) = \sin(y) \sin(20) \sin(40)$

$\tt \dashrightarrow \sin(60) \sin(50 - y) = 2[ \sin(40) \cos(10)] \sin(y)$

Now, Use

$\tt \dashrightarrow\sin(a) \sin(60 - a) \sin(60 + a) = \frac{1}{4} \sin(3a)$

We get, y = 20°.

So,

$\tt \dashrightarrow \angle x = 180 - (20 + 60)$

$\tt \dashrightarrow \angle x =100 \degree$

Therefore, the value of x be 100°.