Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202526 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , with usual notations, if a=5, ~b =7, ~A = 3 4 , then total number of triangles possible are

Options

  1. A1
  2. B0
  3. C2
  4. D5

Correct answer

B. 0

Step-by-step solution

Using the Law of Sines with sides a = 5 , b = 7 , and A = 3 4 , we establish the relation: a A = b B This gives 5 3 4 = 7 B Solving for B : B = 7 3 4 5 = 21 20 Since 21 20 > 1 exceeds the valid range of sine values [-1, 1] , no such angle B exists. Thus, the number of possible triangles is 0 .

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All MHT CET PYQs