Question

Triangle ABC is given where m∠A = 33°, a = 15 in., and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Explain your answer.

Answer 1

2 Triangles can be made with the given measurements

Explanation:

Start by solving for side b

b = 9/sin33 = appr 16.5

9<15<16.5 there are two possible triangles

sin33/15 = sinB/16.5 = sinB=(16.5sin33)/15

B=36.9, 180-36.9=143.1 Next determine if the angles are correct

36.9+33=69.9 143.1+33=176.1 Both of these are less than 180, two triangles can be drawn.