Calculating Triangle Area Using Sides and Angle
The area of a triangle can be calculated when two sides and the angle between them are known. The formula used is:
Area $= \frac{1}{2} ab \sin(C)$
Where 'a' and 'b' are the lengths of the two sides, and 'C' is the measure of the included angle.
Applying the Formula
- Given sides: $a = 8$ cm, $b = 10$ cm
- Given included angle: $C = 120^\circ$
- Substitute these values into the formula:
Area $= \frac{1}{2} \times 8 \text{ cm} \times 10 \text{ cm} \times \sin(120^\circ)$
Calculating the Sine Value
The sine of $120^\circ$ is a standard trigonometric value:
$\sin(120^\circ) = \sin(180^\circ - 60^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2}$
Final Area Calculation
Now, substitute the sine value back into the area calculation:
Area $= \frac{1}{2} \times 8 \times 10 \times \frac{\sqrt{3}}{2}$
Area $= 4 \times 10 \times \frac{\sqrt{3}}{2}$
Area $= 40 \times \frac{\sqrt{3}}{2}$
Area $= 20\sqrt{3} \text{ cm}^2$
The area of the triangle is $20\sqrt{3} \text{ cm}^2$.
Similar Questions
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If p(√3 + cot 30°) = tan3 60° - 2sin 60°, then the value of p is:
Important Questions from Trigonometry
The value of 5 sin 14° sec 76° + 3 cot 15° cot 75° + 2 tan 45° is:
If two complimentary angles are in the ratio of 4 : 5, find the greater angle.
If \(\frac{\sin\spaceθ \space+\space \cos\spaceθ} {\sin \spaceθ \space-\space \cos \spaceθ} = \frac{\sqrt3 \space-\space 1}{\sqrt3 \space+\space 1} \) , then the angle θ is
If tan α = 1/2, tan β = 1/3, then find α + β.
Simplify: sin (A + B) sin (A – B)
