the angle of elevation of the top of the building from a point 30 meters away from the building is 65 degrees
and how high is the building?
h/30= tanTheta
solve for h.
what's the answer ?
To find the height of the building, we can use the concept of trigonometry.
Let's denote the height of the building as "h" and the distance from the point to the building as "d".
From the problem, we know that the angle of elevation (θ) is 65 degrees, and the distance (d) is 30 meters.
Using the trigonometric ratio tangent (tan), we can set up the following equation:
tan(θ) = opposite/adjacent
tan(65) = h/d
Substituting the given values, we have:
tan(65) = h/30
To solve for the height (h), we can isolate it by multiplying both sides of the equation by 30:
30 * tan(65) = h
Using a calculator, we find:
h ≈ 64.84 meters
Therefore, the height of the building is approximately 64.84 meters.
To find the height of the building, we can use trigonometry. The angle of elevation is the angle formed between the horizontal line (the ground) and the line of sight from the observer to the top of the building.
In this scenario, we know the angle of elevation (65 degrees) and the distance from the observer to the building (30 meters). To find the height of the building, we can use the tangent function.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building (unknown), and the adjacent side is the distance from the observer to the building (30 meters).
So, we can write the equation as:
tan(65 degrees) = height of the building / 30 meters
To find the height of the building, we need to isolate the unknown variable (height of the building). Rearranging the equation, we have:
height of the building = 30 meters * tan(65 degrees)
Now, let's calculate the height of the building using a scientific calculator or trigonometric tables:
height of the building = 30 meters * tan(65 degrees)
≈ 30 meters * 2.1445 (rounded to four decimal places)
≈ 64.34 meters (rounded to two decimal places)
Therefore, the height of the building is approximately 64.34 meters.