Home
Class 12
MATHS
In triangle A B C ,D is on A C such that...

In triangle `A B C ,D` is on `A C` such that `A D=B C' and BD=D C ,/_D B C=2x ,a n d/_B A D=3x ,` all angles are in degrees, then find the value of `x

Text Solution

Verified by Experts

In `Delta ABC, (AC)/(sin 5x) = (BC)/(sin 3x)`
`rArr (a + p)/(sin 5x) = (a)/(sin 3 x)`....(i)

In `Delta BDN, cos 2x = (a)/(2p)`
or `a = 2p cos 2x`
From Eq. (i) `(2p cos 2 x + p)/(sin 5 x) = (2p cos 2x)/(sin 3x)`
or `2 sin 3x cos 2x + sin 3x = 2 sin 5x cos 2x`
or `sin 5x + sin x + sin 3x = sin 7 x + sin 3x`
or `sin 7 x - sin 5 x = sin x`
or `2 cos 6x sin x = sin x`
or `cos 6x = (1)/(2)`
`rArr x = 10^(@)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Illustration|86 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.1|12 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D * D B , sin sin A * Sin B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

In triangle A B C ,A D is the altitude from Adot If b > c ,/_C=23^0,a n dA D=(a b c)/(b^2-c^2), then /_B=_____

If a ,b ,c ,and d are in H.P., then find the value of (a^(-2)-d^-2)/(b^(-2)-c^-2) .

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c))+11 is a. -sqrt(3) b. 11-3sqrt(3) c. 11+6sqrt(3) d. 3sqrt(3)

a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

If A : B = 2 : 3 , B : C = 4 : 5 " and " C : D = 6 : 7 , then find A : D .

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2