Final answer:
To calculate the distance from the transit to the top of the building, we can use trigonometry. The tangent of the angle of elevation is equal to the height of the building divided by the distance from the transit to the building. Using this relationship, we can find that the distance is approximately 2.39 meters. To calculate the height of the building, we can use the same trigonometric relationship and find that the height is approximately 1.74 meters.
Step-by-step explanation:
In order to calculate the distance from the transit to the top of the building, we can use trigonometry. The tangent of the angle of elevation is equal to the height of the building divided by the distance from the transit to the building. Let's denote the distance from the transit to the top of the building as x. Using the given information, we can set up the equation:
tan(37°) = height of the building / x
We know that the height of the building is 1.5 m, so we can substitute that into the equation:
tan(37°) = 1.5 m / x
Solving for x, we get:
x = 1.5 m / tan(37°) = 2.39 m
Therefore, the distance from the transit to the top of the building is approximately 2.39 meters.
To calculate the height of the building, we can use the same trigonometric relationship, but this time solve for the height. Rearranging the equation, we have:
height of the building = x * tan(37°)
Substituting in the value of x we found earlier, we get:
height of the building = 2.39 m * tan(37°) = 1.74 m
Therefore, the height of the building is approximately 1.74 meters.