Question

Find the angle θ between the two sides of a triangle whose lengths are 5cm and 4cm , if its area is 5cm²

Answer 1

`\Delta = \frac 1 2 a b \sin C`

`\Delta=5, \quad a=5, \quad b=4`

`\sin C = (2 \Delta)/(ab) = (2 (5))/(5(4) ) = \frac 1 2`

`C=30^\circ \textrm{ or } C=150^\circ`

Answer: two possibilities, θ=30° or 150°