Final answer:
To calculate the horizontal distance and building height, two right-angled triangles based on the observer's eye level and the angles of elevation and depression are created. Trigonometric functions are used to solve for these distances which are then rounded to the nearest meter.
Step-by-step explanation:
To find the horizontal distance of the observer from the building and the height of the building using angles of elevation and depression, we use trigonometric functions. We set up two right-angled triangles: one for the angle of depression to the foot of the building and one for the angle of elevation to the top of the building. The observer's eye level, 2.5 meters above the ground, forms the heights of these triangles.
First, let's handle the angle of depression. The angle of depression to the bottom is 5°. Using the tangent function:
tangent of Angle = Opposite / Adjacent
tan(5°) = 2.5 / Distance to Building
Distance to Building = 2.5 / tan(5°)
For the angle of elevation to the top:
tan(20°) = (Height of Building - 2.5) / Distance to Building
Height of Building = (tan(20°) × Distance to Building) + 2.5
By calculating these values, we can find the horizontal distance and the height of the building accurately. Once found, they can be rounded to the nearest meter as required.