Question

Triangle OBC is a right triangle drawn on a coordinate plane. Side OC lies on the x-axis, the coordinates of point O are (0, 0), and the coordinates of point B are (6, 8).

sin ∠BOC =
tan ∠BOC =

Answer 1

Long leg = 8 → opposite
short leg = 6 → adjacent
hypotenuse = ?

8² + 6² = c²
64 + 36 = c²
100 = c²
√100 = √c²
10 = c

sin ∠BOC = opposite / hypotenuse
sin ∠BOC = 8 / 10
sin ∠BOC = 0.80

tan ∠BOC = opposite / adjacent
tan ∠BOC = 8 / 6
tan ∠BOC = 1.33