Home
Class 12
MATHS
The sides of triangle are in A.P. and th...

The sides of triangle are in A.P. and the greatest angle exceeds the least by `90^(@)`. The sides are in the ratio:

A

` 5 : 9 : 13 `

B

`3 : 4 : 5 `

C

`4 : 5 : 6 `

D

` 5 : 6 : 7 `

Text Solution

Verified by Experts

`a, b, c ` are in A.P
` angle C = 2 angle A rArr sin C = sin 2 A `
` ( sin C ) /( sin A ) = 2 cos A rArr ( c ) /( a ) = 2 ((b ^ 2 + c ^ 2 - a ^ 2 ))/ ( 2bc ) `
Put ` a = b - d , c = b + d, d gt 0 rArr d = (b)/(5) `
` a = (4 ) /(5 ) b, C = (6b ) /(5 ) , a : b : c = 4 : 5 : 6 `
Promotional Banner

Topper's Solved these Questions

  • JEE Main Revision Test-9 | JEE-2020

    VMC MODULES ENGLISH|Exercise SECTION 2|5 Videos

  • JEE Main Revision Test-6 | JEE-2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If the sides of a triangle are in A.P. and the greatest angle of the triangle exceeds the least by 90^(@) , then sine of the third angle is

If the sides of a triangle are in A.P., and its greatest angle exceeds the least angle by alpha , show that the sides are in the ratio 1+x :1:1-x , , where x = sqrt((1- cos alpha)/(7 - cos alpha))

The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles

The angles of a triangle are in A.P. If the greatest angle is double the least, find the angles.

The sides of a triangle are in a ratio of 4:5:6. the smallest angle is

If the lengths of the sides of a triangle are in AP and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is

The sides of a right angled triangle arein A.P. , then they are in the ratio

If the angles of a triangle are in A.P.with common difference equal 1//3 of the least angle ,the sides are in the ratio

The angles of a triangle are in A.P. If the greatest angle is double the least, then the ratio of the angles (in increasing order) is 2:3:4 (b) 1:2:3 (c) 3:4:5 (d) none of these

The angles in a triangle are in A.P. and the ratio of the smallest angle in degrees to the greatest angle in radians is 60:phi Find the angle of the triangle in degrees and radians.