From a point 36 meters from a building and 2.3 meters above the ground, the angle of elevation of the top of the building is observed to be 60°. What is the height of the building?
X = 36 m.
Tan60 = Y/X
Solve for Y.
h = Y + 2.3
Well, let's have some fun with this math problem, shall we?
So, we have a building and someone standing 36 meters away, trying to measure its height. But instead of using a measuring tape, they decide to go with the good old angle of elevation method.
Now, according to the information provided, the angle of elevation to the top of the building is 60 degrees. Since I'm a bot who loves to keep things light-hearted, let's pretend that the building is playing a game of hide-and-seek, and it's decided to hide right up in the sky at an angle of 60 degrees.
Now, let's get back to solving the problem. We can use a little trigonometry here to find the height of the building.
We have the opposite side, which is the height of the building, and we have the adjacent side, which is the distance from the building to the observer. To find the height, we can use the tangent function, which is equal to the opposite side divided by the adjacent side.
So, the tangent of 60 degrees is equal to the height of the building divided by 36 meters.
But wait, we're missing the height! Okay, let's do a little rearranging. We can multiply both sides of the equation by 36 meters to isolate the height.
So, the height of the building is equal to the tangent of 60 degrees times 36 meters.
Now, I could go into the details of calculating the tangent, but that's a little too serious for me. Let's just simplify it and give you the answer!
Drum roll, please...
The height of the building is approximately 62.68 meters. Ta-da!
So, the building decided to come out of hiding and reveal its height. It's a good thing we played along with its little game, otherwise we might have missed it by an angle.
To find the height of the building, we can use the tangent function.
Tangent of an angle is defined as the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the distance from the building to the point of observation.
We can set up the following equation:
tan(angle) = opposite/adjacent
tan(60°) = height of the building / 36 meters
Solving for the height of the building, we have:
(height of the building) = tan(60°) * 36 meters
Using a calculator, we find that tan(60°) is approximately 1.732.
Therefore, the height of the building is:
(height of the building) = 1.732 * 36 meters
Calculating this, we find that the height of the building is approximately 62.352 meters.
To find the height of the building, we can use trigonometry and the concept of the tangent function.
Let's denote the height of the building as h. We are given the following information:
Angle of elevation = 60°
Distance from the building = 36 meters
Height from the ground = 2.3 meters
To solve for h, we can use the tangent function.
Tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the building (36 meters).
Therefore, we can set up the equation:
tan(60°) = h / 36
To solve for h, we need to isolate it on one side of the equation. We can rearrange the equation to solve for h:
h = tan(60°) * 36
Now, we can calculate the value of h:
h = tan(60°) * 36
h ≈ 1.732 * 36
h ≈ 62.352
So, the height of the building is approximately 62.352 meters.