D angle of elevation of a building frm a measuring instruments placed on d ground is 30 degree if d building is 40m high, how far is d instrument frm d foot of d building.
in a 30-60-90 triangle, the sides are 1 and √3. Scale that up by 40, and the sides are 40 and 69.28
d = 69.28 m
Well, well, well! Looks like we have a little trigonometry problem here. Let's put on our thinking caps and solve it, shall we?
We have a building with a height of 40 meters and an angle of elevation of 30 degrees. We want to find the distance between the measuring instrument on the ground and the foot of the building.
Now, if you imagine drawing a right triangle, with the building height as the vertical side, the distance as the horizontal side, and the angle of elevation as the angle, we can use some good old trigonometry. Specifically, we're going to use the tangent function.
Tangent of an angle is equal to the ratio of the opposite side (the height of the building) to the adjacent side (the distance we're trying to find). In this case:
tan(30 degrees) = opposite/adjacent
tan(30 degrees) = 40m / adjacent
Now, let's solve for the adjacent side, which represents the distance:
adjacent = 40m / tan(30 degrees)
Plugging this into a calculator, we find that the adjacent side (distance) is approximately 69.28 meters.
So, my friend, that means the measuring instrument is roughly 69.28 meters away from the foot of the building. Ta-da!
To solve this problem, we can use the concept of trigonometry. Let's denote the distance from the instrument to the foot of the building as x.
In a right-angled triangle, the angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the building.
Based on the given information, we have the following:
Angle of elevation = 30 degrees
Height of the building = 40m
Now, we can use the tangent function, which is defined as the opposite (height of the building) divided by the adjacent (distance from the instrument to the foot of the building). In equation form:
tan(angle of elevation) = height of the building / distance to the building
Using the values we have, we can set up the equation as follows:
tan(30 degrees) = 40m / x
Now we can solve for x. Taking the tangent of 30 degrees:
√3/3 = 40m / x
To isolate x, we can crossmultiply:
x * √3/3 = 40m
Multiplying both sides by 3:
x * √3 = 120m
Now, to get the value of x, we divide both sides by √3:
x = 120m / √3
Using a calculator, we can approximate this value to:
x ≈ 69.28m
Therefore, the instrument is approximately 69.28 meters away from the foot of the building.
To find the distance of the instrument from the foot of the building, we can use trigonometry and the concept of angle of elevation.
Let's denote the height of the building as "h", the distance from the instrument to the foot of the building as "x", and the angle of elevation as "θ" (which is given as 30 degrees in this case).
We can use the tangent function, as tangent(theta) = opposite/adjacent. In this case, the opposite side is the height of the building (h) and the adjacent side is the distance from the instrument to the building (x).
So, we have the equation: tan(θ) = h/x
Substituting the values we have: tan(30 degrees) = 40/x
Now, we can solve for x by rearranging the equation:
x = 40 / tan(30 degrees)
Using a scientific calculator, the tangent of 30 degrees is approximately 0.577.
x = 40 / 0.577
Calculating this gives us:
x ≈ 69.28 meters
Therefore, the instrument is approximately 69.28 meters away from the foot of the building.