Question

euclid has just created a triangle whose longest side is 20. if the length of the other side is 10 cm and the area of triangle is 80 sq. cm, then what is the length of the third side?

Answer 1

Answer:

Step-by-step explanation:

A very simple different approach is to first find the sin of the angle between the sides of the lengths 10 and 20. Then the area formula tells us that (α denotes the angle between those sides)

A=80=12⋅10⋅20⋅sinα=100⋅sinα⟹sinα=0.8

Then by using the fact that cosα=±1−sin2α−−−−−−−−√ and that α is acute, since the side of the length 20 is the longest one, we further have that

cosα=1−sin2α−−−−−−−−√=0.6

By using the Law of Cosines and the fact that a is positive, where a is the unknown side of the triangle, we have that

a=102+202−2⋅10⋅20⋅0.6−−−−−−−−−−−−−−−−−−−−−√=265−−√

Hence the unknown side is  a=265