Question

Question

Determine whether it is possible to construct one, many or no triangle(s) with two side lengths of 3 inches that meet at a 20 degree angle.

one triangle

many triangles

no triangles

Answer 1

One triangle

Explanation:

By the Law of Cosines, given two side lengths of 3 inches and an included angle of 20°, then we are able to get the length of the third side using the formula
`a^2=b^2+c^2+2bc\cos(A)`

Hence, you can construct only one triangle because of SAS Theorem.

Answer 2

We can construct only one triangle with the given description(this triangle is unique).

It is isosceles so the two sides are congruent(

4

4 cm) each. The angle they form is specified

80

°

80° so there is no way to construct one more with the same characteristics(we will have to change the angle or the length of the two sides).

Explanation: