Home
Class 12
MATHS
In triangle A B C ,/B=pi/3,a n d/C=pi/4d...

In triangle `A B C ,/_B=pi/3,a n d/_C=pi/4dot` Let `D` divided `B C` internally in the ratio `1: 3.` Then`(s i N/_B A D)/(sin/_C A B)` equals `1/(sqrt(6))` (b) `1/3` (c) `1/(sqrt(3))` (d) `sqrt(2/3)`

A

`(1)/(sqrt(6))`

B

`(1)/(3)`

C

`(1)/(sqrt(3))`

D

`sqrt((2)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
In `DeltaABD`, applying since rule, we get

`(AD)/(sin pi//3)=(x)/(sin alpha)`
`rArr AD=(3)/(sqrt(2))x sin beta " "....(i)`
and in `DeltaACD`, applying since rule, we get
`(AD)/(sin//pi)=(3x)/(sin beta)`
`rArrAD=(3)/(sqrt(2))x sin beta" "....(ii)` From Eqs. (i) and (ii) , `(sqrt(3)x)/(2 sin alpha)=(3x)/(sqrt(2)sin beta)`
`rArr=(sin alpha)/(sin beta)=(1)/(sqrt(6))`
Promotional Banner

Similar Questions

Explore conceptually related problems

In triangle A B C ,/_B=pi/3,a n d/_C=pi/4dot Let D divided B C internally in the ratio 1: 3. Then (sin/_B A D)/(sin/_C A B) equals (a) 1/(sqrt(6)) (b) 1/3 (c) 1/(sqrt(3)) (d) sqrt(2/3)

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

In triangle A B C , Medians A D and C E are drawn. If A D=5,/_D A C=pi/8,a n d/_A C E=pi/4 , then the area of the triangle A B C is equal to (25)/9 (b) (25)/3 (c) (25)/(18) (d) (10)/3

In a triangle A B C ,/_A=60^0a n db : e=(sqrt(3)+1):2, then find the value of (/_B-/_C)dot

In isosceles triangles A B C ,| vec A B|=| vec B C|=8, a point E divides A B internally in the ratio 1:3, then find the angle between vec C Ea n d vec C A(w h e r e| vec C A|=12)dot

In A B C , the coordinates of B are (0,0),A B=2,/_A B C=pi/3, and the middle point of B C has coordinates (2,0)dot The centroid o the triangle is (a) (1/2,(sqrt(3))/2) (b) (5/3,1/(sqrt(3))) (c) (4+(sqrt(3))/3,1/3) (d) none of these

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If x=1+1/(3+1/(2+1/(3+1/(2oo)))) a sqrt(5/2) b. sqrt(3/2) c. sqrt(7/3) d. sqrt(5/3)