Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate then label all side lengths to the nearest tenth of a centimetre and all angles to the nearest degree.

Question

A) b= 3.0 cm, c=5.5 cm and angle B = 30 degrees

Answer 1

First let's see if it is possible.

Start with a base of BC, sketch an angle of 30° at B and draw a line BA = 3.5
sketch in an altitude from A to BC to meet BC at D
sin30° = AD/3.5
AD = 3.5(1/2) = 1.75
Since AC > 1.75, it will be possible to draw the triangle. As a matter of fact there are two such triangles possible
(With centre at A and radius 3.0, we will be able to draw an arc which will cut BC at two places.
By the Sine Law:
sinC/3.5 = sin30/3
sinC = .58333..
angle C = 35.7° or 180-35.7 = 144.3°

Case1: C = 35.7 , then A = 114.3°
Case2: C = 144.3, then A = 5.7°

Use the sine law to find BC for each case.

This is called the ambigious case of the sine law, usually resulting in the data given as SSA

Answer 2

I misread your c = 5.5 as c = 3.5 , sorry about that

So AD should be 2.75
But AC is still greater than 2.75

so no real harm done, all you have to do is change the 3.5 to 5.5 and use the new values.

The conclusion is still the same, but make sure you get the new angles.