Question

DUE SOON PLEASE SOME HELP! DUE IN HALF HOUR SO CONFUSED PLEASE PLEASE HELP! QUESTION DOWN BELOW!!!

Answer 1

This is a ssa situation, no triangle is possible.

Explanation:

"SSA" means "Side, Side, Angle".

In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.

In triangle XYZ:

• X, Y and Z are the interior angles.
• x, y and z are the sides opposite the corresponding interior angles.

Given:

• m∠X = 55°
• side x = 12 cm
• side y = 39 cm

The angle that is between the sides x and y is angle Z.

Therefore, as angle X is not the angle between the given sides, ΔXYZ is an SSA triangle.

Law of Sines

`\sf (\sin X)/(x)=(\sin Y)/(y)=(\sin Z)/(z)`

(where X, Y and Z are the angles and x, y and z are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle Y:

`\implies \sf (\sin 55^(\circ))/(12)=(\sin Y)/(39)`

`\implies \sf \sin Y=(39\sin 55^(\circ))/(12)`

`\implies \sf \sin Y=2.6622441...`

As -1 ≤ sin Y ≤ 1, there is no solution for angle Y.

Therefore, although this is an SSA situation, no triangle is possible.