Home
Class 12
MATHS
In a triangle ABC, angle A = 60^(@) and ...

In a triangle ABC, `angle A = 60^(@) and b : c = (sqrt3 + 1) : 2`, then find the value of `(angle B - angle C)`

Text Solution

Verified by Experts

`(b)/(c) = (sqrt3 + 1)/(2) rArr (b - c)/(b + c) = (sqrt3 + 1 -2)/(srt3 + 1 + 2) = (sqrt3 -1)/((sqrt3 + 1)) (1)/(sqrt3)`
Now using `tan.(B - C)/(2) = (b - C)/(b + c) cot. (A)/(2)`, we get
`tan.(B - C)/(2) = (sqrt3 - 1)/((sqrt3 + 1)) = 2 - sqrt3 rArr (B - C)/(2) = 15^(@)`
`:. B - C = 30^(@)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC,/_A=60^(@) and b:e=(sqrt(3)+1):2 then find the value of (/_B-/_C)

If the angles of a triangle ABC are in AP and b:c=sqrt3:sqrt2 the what is the measure of angle A?

In a right triangle ABC, right-angled at B, if sin (A - C) = (1)/(2) find the measures of angles A and C

In triangle ABC, right-angled at B. if tan A = 1/sqrt(3) ,find the value of: sin A cos C+cos A sin C

In a triangle ABC a= 4 , b= 3 , angle A =60 ^@ ,Then c is root of equation :-

The angles of triangle ABC are in A.P. and b:c= sqrt(3):sqrt(2) find angle A , angle B , angle C .

In a Delta ABC , angle A + angle B = 118^@ angle A + angle C = 96^@ . Find the value of angle A