Home
Class 12
MATHS
If in triangle ABC, a = (1 + sqrt3) cm, ...

If in triangle `ABC, a = (1 + sqrt3) cm, b = 2 cm, and angle C = 6` then find the other two angles and the third side

Text Solution

Verified by Experts

The correct Answer is:
`c = sqrt(6), angleA = 45^(@)` and `angleA = 45^(@)`
Given that ,
`a=1+sqrt(3)b=2 and angle C=60^(@)`
We have, `c^(2)=a^(2)+b^(2)-2ab cos C`
`rArr c^(2)=(1+sqrt(3))^(2)+4-2(1+sqrt(3))*2 cos 60^(@)`
`rArr c^(2)=1+2sqrt(3)+3+4-2-2sqrt(3)`
`rArr c^(2)-6`
`rArr c= sqrt(6)`
Using sin rule,
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`
`rArr (1+sqrt(3))/(sinA)=(2)/(sinB)=(sqrt(6))/(sin 60^(@))`
`:. sin B=(2 sin 60^(@))/(sqrt(6))=(2xx(sqrt(3))/(2))/(sqrt(6))=(1)/(sqrt(2))`
`rArr =B=45^(@)`
` :. A=180^(@)-(60^(@)+45^(@))=75^(@)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/_C=60^0 , then find the other two angles and the third side.

In Delta ABC, if a = sqrt(3) - 1, b = sqrt(3) + 1 and angleC = 60^(@) , find the other side and the other two angles.

In Delta ABC AB = 6 sqrt 3 cm,AC = 12 cm, BC = 6 cm."Find measure of" angle A

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)) , then find the greatest angle

Solve the triangle ABC if a=5 , b=4 and angle A =60^(@ , then side c is