## Sure, I can help you find the base of the triangle using the given angles. In a right triangle with one angle being 90 degrees, you can use the trigonometric ratios to find the lengths of the sides.

Since you have a right triangle with angles measuring 30 degrees and 60 degrees, this means you have a 30-60-90 triangle. In a 30-60-90 triangle, the sides are in a special ratio. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is the length of the hypotenuse multiplied by the square root of 3.

In your case, if the height of the triangle (opposite the 60-degree angle) is 5, the length of the hypotenuse is 2 times the height, which is 10. And the base of the triangle (opposite the 30-degree angle) is the length of the hypotenuse multiplied by the square root of 3, which is 10 * âˆš3.

Now you can compare the area of the triangle to 25 times the square root of 3. The area of a triangle can be found using the formula A = 1/2 * base * height. Plug in the values you have: base = 10 * âˆš3 and height = 5. Calculate:

A = 1/2 * (10 * âˆš3) * 5

= 25âˆš3

So, the area of the triangle is 25 times the square root of 3, which means the two values are equal.

To recap, in a 30-60-90 triangle, you can determine the length of the base (opposite the 30-degree angle) using the length of the height (opposite the 60-degree angle) by multiplying the height by the square root of 3.