Question

Find the exact value of x and y in the following special right angle.

Answer 1

In a 30-60-90 right triangle, the side lengths are in a specific ratio: 1:√3:2. Given that the hypotenuse corresponds to the 60 degrees angle and has a length of 10 units, we can use this information to find the lengths of the other sides.

Let x be the shorter leg (opposite the 30 degrees angle) and y be the longer leg (opposite the 60 degrees angle).

The ratio for a 30-60-90 triangle is:

`\[ \text{Shorter leg} : \text{Hypotenuse} : \text{Longer leg} = 1 : √(3) : 2 \]`

So, in this case:

`\[ x : 10 : y = 1 : √(3) : 2 \]`

To find x and y, we can set up equations:

`\[ x = (1)/(√(3)) * 10 \]`

`\[ y = 2 * 10 \]`

Simplifying these expressions gives:

`\[ x = (10)/(√(3)) \]`

`\[ y = 20 \]`

Therefore, the exact values are
`\( x = (10)/(√(3)) \)` units and y = 20 units.