The angle of elevation from two points A and B to the top of a storey building are 48° and 57°respectively .if AB=50m and the point A and B are opposite each other; calculate;
A.The distance of point A to the building
B.The height of the building
Let's label the point of the top of the building as C.
A: Angle of elevation from point A to point C = 48°
B: Angle of elevation from point B to point C = 57°
AB = 50m (the distance between points A and B)
Since A and B are opposite each other, we can consider triangle ABC.
To find the distance of point A to the building, we can use the tangent function:
tan(48°) = AC / AB
AC = AB * tan(48°) = 50m * tan(48°) ≈ 50m * 1.1106 ≈ 55.53m
The distance of point A to the building is approximately 55.53m.
To find the height of the building, we can use the tangent function again:
tan(57°) = BC / AB
BC = AB * tan(57°) = 50m * tan(57°) ≈ 50m * 1.5402 ≈ 77.01m
The height of the building is approximately 77.01m.