Hello Jiskha-hope you can help me here!

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the horizontal. Find the height of the hill?

sin 12 = h/2500

h = 2500 sin 12 = 520 feet

To find the height of the hill, we can use trigonometry, specifically the sine function.

First, let's define the given information:
- Length of the road (base of the triangle): 2500 feet
- Angle between the road and the horizontal (angle of elevation): 12 degrees

We can set up a right triangle with the road as the base, the height of the hill as the opposite side, and the hypotenuse connecting the top of the hill to the end of the road.

The sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.

Using the given information, we know that:
sin(12 degrees) = height of the hill / length of the road

Now, we can solve for the height of the hill by rearranging the equation and plugging in the known values:
height of the hill = sin(12 degrees) * length of the road
height of the hill = sin(12 degrees) * 2500 feet

To compute this value, we can use a calculator or refer to a table of trigonometric values. Let's calculate it:

sin(12 degrees) = 0.2079 (rounded to four decimal places)
height of the hill = 0.2079 * 2500 feet
height of the hill ≈ 519.75 feet

Therefore, the height of the hill is approximately 519.75 feet.

To find the height of the hill, we can use trigonometry. Specifically, we can use the sine function.

The sine function relates the opposite side of a right triangle to the hypotenuse. In this case, the opposite side is the height of the hill, and the hypotenuse is the length of the road.

The formula to find the height using the sine function is:

height = length * sin(angle)

Let's substitute the given values into the formula:

height = 2500 feet * sin(12 degrees)

To evaluate this expression, you can use a scientific calculator or an online calculator that has a sine function. Simply enter 12 degrees, press the sine function button, and then multiply the result by 2500.

The height of the hill should be approximately 516.14 feet.