Solve the triangle. Angle A is opposite side a, Angle B is opposite side b, and angle C is opposite side c. Round final answers to nearest 10th
Given data : side a = 18, side c = 27, angle A = 29 degrees.
Solving a Triangle:
A triangle is a convex polygon having three sides and three angles. Solving a triangle means finding the value of three of the six measurements when we know three of these measurements. The six measurements in a triangle are the lengths of three sides and the measure of three angles. In the given three measurements one of them must be the length of the side because by only knowing the angles we cannot find the length of the sides.
For solving the triangles we generally use the law of sines which states that sinAa=sinBb=sinCc
where, A,B,C
denotes the measurements of angles of the triangle and a,b,c
denotes the lengths of the sides opposite to the angles respectively.
Another important law used is the law of cosines which directly gives equations that relate the cosine ratio of an angle and lengths of the sides. It is a generalization of the Pythagoras theorem. It is given as, c2=a2+b2?2abcosCa2=b2+c2?2bccosAb2=a2+c2?2accosB