If the side opposite a 60-degree angle in a 30-60-90 right triangle is 73–√ cm long, how long is the hypotenuse?
7cm
28cm
14cm
7 square root of 3cm
In a 30-60-90 right triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse.
Let's assume the length of the hypotenuse is x cm. Therefore, the length of the side opposite the 30-degree angle is x/2 cm.
According to the given information, the length of the side opposite the 60-degree angle is 73 - √ cm.
So, we can set up the following equation:
73 - √ = x/2
To solve for x, we need to isolate it on one side of the equation. Let's start by adding √ to both sides:
73 = x/2 + √
Now, let's multiply both sides by 2 to eliminate the fraction:
146 = x + 2√
Finally, let's subtract 2√ from both sides:
146 - 2√ = x
So, the length of the hypotenuse is 146 - 2√ cm.
Therefore, the correct answer is: 146 - 2√ cm.