Coaching Centre
Area of a triangle
The formula Area = ½ab sin C for any triangle given two sides and the included angle, and finding an unknown side or angle from the area.
The formula
$C$ must be the angle between sides $a$ and $b$.
Find the area of a triangle with sides $8$ and $11$ and included angle $35^\circ$.
A triangle has sides $10$ and $12$ and area $30$. Find the included angle if it is obtuse.
Sides $8$ and $11$, included angle $35^\circ$. Area (2 d.p.)?
$44\sin 35^\circ$.
Sides $10$ and $12$, area $30$. Obtuse included angle?
$\sin C = 0.5$.
Sides $6$ and $9$, included angle $120^\circ$. Area (2 d.p.)?
$27\sin 120^\circ$.
Sides $10$ and $12$, included angle $150^\circ$. Area?
$60 \times 0.5$.
Sides $6$ and $8$, included angle $90^\circ$. Area?
$\tfrac{1}{2} \times 48$.
Area $25$, one side $5$, included angle $90^\circ$. The other side?
$25 = \tfrac{1}{2}(5)b$.
Equilateral triangle with side $6$. Area (2 d.p.)?
$18\sin 60^\circ = 9\sqrt{3}$.
To use $\tfrac{1}{2}ab\sin C$ you need:
The included angle.
New numbers every time. Keep going until you get five in a row.