The computations to find the other two side lengths are summarized in the following table.
Points
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Length
B( -1, -5) and C( -6, -5)
BC = sqrt(( -6-( -1))^2 + ( -5-( -5))^2)
BC = 5
B( -1, -5) and D( -1, 2)
BD = sqrt(( -1-( -1))^2 + ( 2-( -5))^2)
BD = 7
Since BC^2+BD^2 = CD^2, we conclude that △ BCD is a right triangle with ∠B being the right angle.
Next, applying the tangent ratio, we can write the following equation involving the measure of ∠C.
tan C = BD/BC
⇒
tan C = 7/5
Finally, applying the inverse tangent and a calculator, we will find the required measure.
m∠C = arctan (7/5) ≈ 54.5^(∘)
