Question

I need help on this problem too and help pls

Answer 1

The length of leg m is
`$5√(3)$` and the measure of the missing angle in the triangle is 30 degrees.

The diagram shows a right triangle with an angle of 60 degrees. The hypotenuse of the triangle is labeled
`$5√(3)$` and the other two legs are labeled m and n. The length of the leg opposite the 60-degree angle is labeled 2.5.

We can use the Pythagorean Theorem to find the length of the other leg:

`m^2 + n^2 = (5√(3))^2`

`m^2 + n^2 = 75\\m^2 = 75 - n^2`

We can also use the trigonometric ratio of tan to find the length of leg m:

`tan 60 = (m)/(n)`

`m = n * √(3)`

Substituting this into the equation
`$m^2$`, we get:

`(n * √(3))^2 = 75 - n^2`

3n^2 = 75

n^2 = 25

n = 5

Now that we know the length of leg n, we can find the length of leg m using the equation we derived earlier:

`m = n * √(3)\\m = 5 * √(3)\\m = 5√(3)`

Therefore, the length of leg m is
`$5√(3)$`.

We can also find the measure of the missing angle in the triangle using the following equation:

180 - 60 - 90 = 30

Therefore, the missing angle in the triangle measures 30 degrees.