Question

Law of sines: ( sin(A)/a = sin(B)/b = sin(C)/c ). How many distinct triangles can be formed for which ( m∠ A = 75° ), ( a = 2 ), and ( b = 3 )?

a) 0
b) 1
c) 2
d) 3

Answer 1

There is 1 distinct triangle that can be formed for the given values of m∠A, a, and b.

Step-by-step explanation:

To determine the number of distinct triangles, we can use the Law of Sines. The Law of Sines states that sin(A)/a = sin(B)/b = sin(C)/c. Given that m∠A = 75°, a = 2, and b = 3, we can substitute these values into the equation. We have sin(75°)/2 = sin(B)/3. Solving for sin(B), we find that sin(B) = 2sin(75°)/3. Since sin(B) is a positive value, we know that B is an acute angle and not 180°-B. Therefore, there is 1 distinct triangle that can be formed for the given values of A, a, and b.