Question

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.

a) b=3.0cm, c=5.5cm, ∠ B=30°
b) b=12.2cm, c=8.2cm, ∠ C=34°
c) a=11.1cm, c=5.2cm, ∠ C=33°

Answer 1

a) It is possible to draw a triangle with the given information.

b) It is not possible to draw a triangle with the given information.

c) It is possible to draw a triangle with the given information.

Step-by-step explanation:

In the first scenario a we can use the Law of Sines to determine the missing side a. Using the formula a/\sin A= b/\sinB = c/\sin C where A is the angle opposite side a we find a approx 5.2 cm. Therefore a triangle with side lengths a=5.2 cm b=3.0 cm and c=5.5 cm and angles A approx 52^circ B=30^circ and C=98^circ is possible.

In the second scenario b the sum of angles C=34^circ and B exceeds 90^circ since A = 180^circ - B - C violating the Triangle Inequality Theorem. Thus, it is not possible to form a triangle with side lengths
`(b=12.2\) cm, \(c=8.2\` cm and angle
`\(C=34^\circ\)`.

In the third scenario c using the Law of Sines we find side b approx 8.7 cm. Therefore a triangle with side lengths a=11.1cm b=8.7 cm and c=5.2 cm and angles A approx 44^circ B=103^circ\ and C=33^circ is possible.