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
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