A 10 ft. ladder is leaning against a building and makes an angle of 65 degrees with the ground. How high above the ground is the top of the ladder?

jkk

Well, I can tell you that the ladder is definitely reaching new heights with that angle! But to answer your question, let's use a little bit of trigonometry.

The height the ladder reaches can be calculated using the equation: height = ladder length * sin(angle)

So in this case, the height = 10 ft * sin(65 degrees). Punching in the numbers, we get:

height = 10 ft * 0.9063 (approximately) = 9.06 ft (approximately)

So, the top of the ladder is approximately 9.06 feet above the ground. Keep reaching for the stars, ladder!

To find the height above the ground, we can use trigonometry. Let's call the height "h".

In this case, the ladder is the hypotenuse of a right triangle, and the ground represents one of the legs. The angle between the ladder and the ground is 65 degrees.

Using the sine function, we can write the equation as:

sin(65 degrees) = h / 10 ft.

To solve for "h", we multiply both sides by 10 ft:

h = 10 ft * sin(65 degrees)

Using a calculator, we find that sin(65 degrees) ≈ 0.9063.

Plugging the value back into the equation:

h = 10 ft * 0.9063

Simplifying:

h ≈ 9.06 ft

Therefore, the top of the ladder is approximately 9.06 feet above the ground.

To find the height above the ground at which the top of the ladder is located, we need to use trigonometric functions. In this case, we can use the sine function.

The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse, which is the longest side in a right-angled triangle. In this scenario, the height of the ladder (opposite side) is what we want to find, and the length of the ladder itself is the hypotenuse.

Given that the ladder is 10 ft. long and makes an angle of 65 degrees with the ground, we can use the sine function to solve for the height:

sin(65°) = height / 10 ft.

Let's calculate it:

sin(65°) = 0.90630778703 (rounded to 11 decimal places)

Now, we can solve for the height:

height = sin(65°) * 10 ft.

height ≈ 0.90630778703 * 10 ft.

height ≈ 9.063 ft.

Therefore, the top of the ladder is approximately 9.063 feet above the ground.

Draw a right triangle, with 65° with the horizontal.

The ladder is the hypotenuse, and the wall is the opposite side of the 65° angle.

The height of the top of the ladder is therefore
h=Lsin(65°)
where L is the length of the ladder.