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
- If $\sin(x) = 0.6$ and $x \in (0, \pi/2)$, find $\sin(2x) + \cos(2x)$.
- If $\cos A = 1 - 2\sin^2A$, then what is the value of $\cos 2A$?
- If $\sin(3x + 10^{\circ}) = \cos(2x - 5^{\circ})$, find x.
- If $\sin(A) = \cos(B), \cos(A) = \sin(C)$, and $A + B + C = 90^\circ$, then what is the value of angle A?
- If $\sin A = 0.6$ and $\cos A = 0.8$, what is $\tan A$?
- If $\sin A = 0.6$, what is the value of $\tan A$ ?
- If $\sec A + \tan A = p$, then what is $\sec A$ in terms of p?
- Which of the following is true for all acute angles A?
- If $\tan x = \cot(3x - 30^\circ)$, find $x$.
Important Questions from Trigonometry
The given equation can be reduced to
If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?
Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180 / π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π / 9 results. The angle θ must be equal to
What is sin 2α equal to?
If \(\sin θ = \frac{8}{{17}}\) , then find the value of tan θ.
