Explanation:
the area of a right-angled triangle is
leg1 × leg2 / 2 =
sin(angle)×baseline × cos(angle)×baseline / 2 =
sin(angle)×cos(angle) × baseline² / 2
4 = sin(30)×baseline = 0.5 × baseline
baseline = 4/0.5 = 8 units
Pythagoras gives us the third side = cos(30)×baseline :
8² = 4² + side²
64 = 16 + side²
48 = side²
side = sqrt(48) = sqrt(16×3) = 4×sqrt(3) units
so, the area of the triangle is again
sin(30)×baseline × cos(30)×baseline / 2 =
= 4 × 4×sqrt(3) / 2 = 2×4×sqrt(3) = 8×sqrt(3) units² =
= 13.85640646... units²