I have a right angled triangle and I am given the following information;
I have two angles, one is the normal 90 degree angle and the other angle is 65 degrees in the opposite vertex.
I am told that the right angled triangle has a parallel line to BC.
To imagine the triangle the 90 degrees corner is on the lower left and the 65 degrees is on the lower right vertex. The parallel line is 5 cm long and I am asked to find the length of the side AB, which is the adjacent side of a right angled triangle.
I have used the tan rule;
tan 65 = AB / MN
AB / MN = tan 65
tan 65 = AB / MN = 2.145
muliplied both sides by 5
AB = 2.145 x 5
AB = 10.7 cm (1dp)
My confusion is whether I used the right sin rule as the cosine rule would give an answer of 11.8 cm
They are both close to each other in their solutions, could somebody please advise how I determine the right cosine rule to use when working with parallel lines in triangles please.