A ladder 5 meter long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with the ground. how high up the wall does it reach?

Question

An empty city street during the day. A red brick apartment house stands tall on the right side of the image. Situated against its wall, a silver 5-meter long ladder leans, forming a 50 degree, 32-minute angle with the uneven gray cobblestone ground. The upper end of the ladder reaches high up on the building, creating an interesting visual representation of geometry in the real world context, without any visible text.

A ladder 5 meter long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with the ground. how high up the wall does it reach?

Answer 1

sin theta = H / L = H / 5

H = 5 * sin theta = 5 * sin 50 ° 32 ´

H = 5 * 0.77199

H = 3.85995 m approx. H = 3.86 m

Answer 2

Well, if I were a ladder, I would have definitely reached for the stars! But in this case, we have a ladder leaning against a wall, not reaching for the stars. So, let's figure out how high up the wall it goes.

Since the ladder forms an angle with the ground, we can use some trigonometry to solve this problem. The ladder acts as the hypotenuse of a right triangle, where the height of the wall is the opposite side.

Now, the angle is given as 50 degrees and 32 minutes, which we can convert to decimal degrees. There are 60 minutes in a degree, so we can write it as 50 + (32/60) degrees.

Calculating this, we get 50.5333 degrees (approximately).

Using the sine function (sin), we can find the height of the wall:

height = ladder length * sin(angle)

height = 5 * sin(50.5333)

height ≈ 3.876 meters

So, the ladder reaches approximately 3.876 meters up the wall.

Answer 3

To find out how high up the wall the ladder reaches, we can use trigonometry. The angle formed by the ladder with the ground is 50 degrees and 32 minutes.

First, we need to convert the angle from minutes to degrees. There are 60 minutes in a degree, so 32 minutes is equal to 32/60 = 0.5333 degrees.

Now we can use the sine function to calculate the height. The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the height of the wall and the hypotenuse is the length of the ladder.

So, we have:

sin(angle) = opposite/hypotenuse

sin(50.5333 degrees) = height/5 meters

To find the height, we can rearrange the equation:

height = sin(50.5333 degrees) * 5 meters

Using a calculator, sin(50.5333 degrees) is equal to approximately 0.7800.

Therefore, the height of the ladder on the wall is:

height = 0.7800 * 5 meters

height = 3.9 meters

So, the ladder reaches a height of 3.9 meters up the wall.

Answer 4

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

First, convert the angle to decimal form. Since there are 60 minutes in a degree, we divide 32 by 60 to get 0.5333 degrees.

Next, we can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. In this case, the opposite side is the height of the wall, and the hypotenuse is the length of the ladder.

So, we can set up the equation:

sin(angle) = height / length of ladder

Substituting the values:

sin(50.5333 degrees) = height / 5 meters

Now, we can solve for the height:

height = sin(50.5333 degrees) * 5 meters

Using a calculator or trigonometric table, find the sine of 50.5333 degrees and multiply it by 5 meters to get the height.

By following these steps, you can find the height up the wall that the ladder reaches.