A ladder leaning against a wall makes a 75º angle with the ground. The base of the ladder is 5.0 feet from the wall. How high up the wall does the ladder reach?

h = 5.0 ft * tan(75º)

To find out how high up the wall the ladder reaches, we can use trigonometry.

Let's call the height up the wall "h". The angle between the ladder and the ground is 75º, so the angle between the wall and the ground is 90º - 75º = 15º.

Using the sine trigonometric function:

sin(15º) = opposite/hypotenuse

We know that the opposite side is "h" and the hypotenuse is the length of the ladder, which is given as 5.0 feet.

sin(15º) = h/5.0

To solve for "h", we can rearrange the equation:

h = 5.0 * sin(15º)

Using a calculator, we can evaluate sin(15º) to be approximately 0.2588.

h = 5.0 * 0.2588

h ≈ 1.294 feet

Therefore, the ladder reaches approximately 1.294 feet up the wall.

To find out how high up the wall the ladder reaches, we can use trigonometry. In this case, we can use the sine function.

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the height of the wall is the side opposite the angle, and the ladder is the hypotenuse.

We know that the angle is 75º and the base of the ladder is 5.0 feet. To use the sine function, we need to measure the length of the hypotenuse.

To find the length of the hypotenuse, we can use the cosine function. The cosine of an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Using the cosine function, we can find the length of the hypotenuse:

cos(75º) = adjacent/hypotenuse

Since the adjacent side is the base of the ladder and its length is 5.0 feet:

cos(75º) = 5.0 feet/hypotenuse

Now, rearranging the equation to solve for the length of the hypotenuse:

hypotenuse = 5.0 feet / cos(75º)

Using a calculator, we can find that cos(75º) is approximately 0.2588 (rounded to four decimal places):

hypotenuse = 5.0 feet / 0.2588 ≈ 19.32 feet

Therefore, the length of the ladder (hypotenuse) is approximately 19.32 feet.

Now, we can find the height of the wall using the sine function:

sin(75º) = opposite/hypotenuse

Substituting the known values:

sin(75º) = height of the wall / 19.32 feet

Rearranging the equation to solve for the height of the wall:

height of the wall = sin(75º) * 19.32 feet

Using a calculator, we can find that sin(75º) is approximately 0.9659 (rounded to four decimal places):

height of the wall = 0.9659 * 19.32 feet ≈ 18.66 feet

Therefore, the ladder reaches approximately 18.66 feet up the wall.