From a window 20 feet above the ground, the angle of elevation to the top of a building across the street is 78°, and the angle of depression to the base of the same building is 15°. find the height of the building across the street.\

The answer would be 371.16 ft.

Refer to the diagram for the scenario. The drawing is not to scale.

Notice the diagram that you will find to adjacent right triangles. All you need to do is first solve for the needed side of one triangle, by using one side.

It sounds confusing I know, but let's do this step by step.

Angle of depression is 15°.

We use this first because we do not have enough data to use the angle of elevation.

To get the adjacent side, we use the trigonometric function TOA which means:

We use the height of the first building as our reference, so our given will be:

Opposite = 20ft

θ = 15°

Now we put that into our formula:

Now that we have that we can solve for the height from the point of 20ft. We use the same formula, because we are looking for the opposite, given the adjacent.

Now that's the height from the top of the first building. To get the total height of the building we just add the 20ft.

351.16ft + 20 ft = 371.16ft

The building across the street is 371.16 ft tall.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.