Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

IN triangle ABC ,angle A is twice the angle B .show that aXa=b(b+c),where a,b,c are sides opposite to angleA,B,C respectively
 
Asked by satishsingh881 | 22 Sep, 2014, 11:20: PM
answered-by-expert Expert Answer
T h e space a b o v e space s u m space i s space t o space b e space s o l v e d space b y space u sin g space sin e space r u l e L e t space angle B equals x comma space angle A equals 2 x comma space angle C equals 180 degree minus 3 x fraction numerator a over denominator sin space A end fraction equals fraction numerator b over denominator sin space B end fraction equals fraction numerator c over denominator sin space C end fraction o r comma space fraction numerator a over denominator sin space 2 x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator sin left parenthesis 180 minus 3 x right parenthesis end fraction o r comma fraction numerator a over denominator 2 sin space x. cos space x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator sin space 3 x end fraction o r comma fraction numerator a over denominator 2 sin space x. cos space x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator 3 sin space x minus 4 sin cubed x end fraction o r comma fraction numerator a over denominator 2 cos space x end fraction equals b equals fraction numerator c over denominator 3 minus 4 sin squared x end fraction space left square bracket M u l t i p l y i n g space b y space sin space x space o n space a l l space t h e space t h r e e space t e r m s right square bracket space l e t space fraction numerator a over denominator 2 cos space x end fraction equals b o r comma space cos space x equals fraction numerator a over denominator 2 b end fraction............. left parenthesis i right parenthesis l e t space b equals fraction numerator c over denominator 3 minus 4 sin squared x end fraction o r comma space 3 minus 4 sin squared x equals c over b o r comma space 3 minus 4 left parenthesis 1 minus cos squared x right parenthesis equals c over b o r comma space 3 minus 4 plus 4 space cos squared x equals c over b o r comma space 4 space cos squared x equals c over b plus 1 o r comma space cos squared x equals fraction numerator c plus b over denominator 4 b end fraction S u b s t i t u t i n g space cos space x space i n space t h e space a b o v e space e q u a t i o n comma o r comma space fraction numerator a squared over denominator 4 b squared end fraction equals fraction numerator c plus b over denominator 4 b end fraction o r comma space a squared over b equals c plus b space space space space space space space left square bracket space because b not equal to 0 right square bracket o r comma space a squared equals b left parenthesis b plus c right parenthesis
Answered by Prasenjit Paul | 23 Sep, 2014, 10:26: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
find area
question image
Asked by kashinigam382 | 05 Jan, 2024, 04:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The areas of two similar triangles are 49 cm2 and 64 cm2 respectively. The ratio of their corresponding sides is ____.
Asked by priyanujt35 | 27 Jul, 2020, 09:13: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
pl solve this sum
question image
Asked by NSSORATHIYA sorathiya | 08 Mar, 2020, 10:16: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Ij triangle ABC and BDE are equilateral triangles where D is the mid point of BC find the ratio of areas of triangle ABC BDE  
Asked by Sangsangapalian | 21 Sep, 2019, 09:34: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
  Two chords AB and CD of a circle meet at E inside the circle as shown in the figure, such that begin mathsize 12px style EC over AE equals BE over ED equals 1 third end style, begin mathsize 12px style angle BAC equals 50 degree. space Find space fraction numerator straight A left parenthesis increment AEB right parenthesis over denominator straight A left parenthesis increment DEC right parenthesis end fraction. end style
Asked by Topperlearning User | 05 Oct, 2017, 08:12: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Perimeters of two similar triangles ABC and DEF are in the ratio 3 : 4. Prove that the ratio of their areas is 9 : 16
Asked by Topperlearning User | 03 Oct, 2017, 01:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Perimeters of two similar triangles ABC and PQR  are in the ratio 4 : 5. If the sum of their areas is 164 cm2, find the area of each triangle.
Asked by Topperlearning User | 03 Oct, 2017, 01:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The areas of two similar triangles ABC and PQR are in the ratio 4 : 9. If the sum of the perimeters is 30 m, find the perimeter of each triangle.
Asked by Topperlearning User | 03 Oct, 2017, 01:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
A student needs 5 paper triangles for some craft work such that side of the second triangle are twice the sides of the first triangle, sides of the third triangle are twice the sides of the second triangle and so on.. Find the ratio of areas of the first and the fifth triangles.
Asked by Topperlearning User | 03 Oct, 2017, 01:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
  An equilateral triangle is based on the side of a square of area 64 sq. cm and another on the diagonal of the same square. Find the ratio of their areas.
Asked by Topperlearning User | 03 Oct, 2017, 01:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×