Choose Yes or No to tell whether there is more than one way to draw a triangle with the given measures. AB = 15 cm, BC = 20 cm, ∠B = 40° AB = 20 cm, AC = 15 cm, ∠C = 40° BC = 10 cm, AB = 5 cm, ∠A = 20° AC = 5 cm, BC = 10 cm, AB = 14 cm

Question:

a. AB = 15 cm, BC = 20 cm, ∠B = 40°

b. AB = 20 cm, AC = 15 cm, ∠C = 40°

c. BC = 10 cm, AB = 5 cm, ∠A = 20°

d. AC = 5 cm, BC = 10 cm, AB = 14 cm

Answer:

The correct options are;

a. No

b. Yes

c. Yes

d. No

Step-by-step explanation:

a. AB = 15 cm, BC = 20 cm, ∠B = 40°

No

The above dimensions include two sides and an included angle, therefore, the triangle is well defined, such that the dimensions of the third side can be found by the given information using cosine rule

b. AB = 20 cm, AC = 15 cm, ∠C = 40°

Yes,

The above dimensions include two sides and a non included angle, therefore, the triangle is not well defined, such that the third side and the other two angles can be made to to make up to a different triangular configuration can be made

c. BC = 10 cm, AB = 5 cm, ∠A = 20°

Yes

The above triangle could be made into one of two triangles

d. AC = 5 cm, BC = 10 cm, AB = 14 cm

No

The above triangle is well defined with all side dimensions known and the angles can be found by cosine rule.