Triangle Problem Setup
We are analyzing a right-angled triangle named ABC, where angle C is the right angle (90°).
- Given Angle A = 60°
- Given side AC (adjacent to Angle A) = $20\sqrt{3}$ units
- The goal is to find the length of the hypotenuse AB.
Trigonometry Application
In a right-angled triangle, the cosine function relates the angle, the adjacent side, and the hypotenuse:
$cos(Angle) = Adjacent / Hypotenuse$
Applying this to Angle A:
$\cos(A) = \frac{AC}{AB}$
Calculation Steps
Substitute the known values into the formula:
$\cos(60^\circ) = \frac{20\sqrt{3}}{AB}$
Recall the value of $\cos(60^\circ)$, which is $\frac{1}{2}$.
So, the equation becomes:
$\frac{1}{2} = \frac{20\sqrt{3}}{AB}$
Rearrange the equation to solve for AB:
$AB = 2 \times 20\sqrt{3}$
$AB = 40\sqrt{3}$
Result
The length of the hypotenuse AB is $40\sqrt{3}$ units.
Similar Questions
- If $r\sin\theta = \frac{7}{2}$ and $r\cos\theta = \frac{7\sqrt{3}}{2}$, then what will be the value of r?
- If $\sin(3x - 20)^\circ = \cos(20 - 3y)^\circ$, then value of x - y will be:
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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.
