What is the line of sight in heights and distances?

The line of sight is the straight line drawn from the observer's eyes to the point being viewed on an object. It is crucial for determining angles of elevation and depression.

Define the angle of elevation.

The angle of elevation is the angle formed by the line of sight to an object above the horizontal level. It helps in calculating the height of objects using trigonometric ratios.

Define the angle of depression.

The angle of depression is the angle formed by the line of sight to an object below the horizontal level. It is used to find the distance to objects below the observer.

What is the formula for calculating the height of an object using the angle of elevation?

The height can be calculated using the formula: height = distance * tan(angle of elevation). For example, if the distance is 30 meters and the angle is 45 degrees, height = 30 * tan(45) = 30 meters.

How do you find the distance to an object when given its height and angle of elevation?

Distance can be calculated using the formula: distance = height / tan(angle of elevation). If the height is 10 meters and the angle is 30 degrees, distance = 10 / tan(30) = 10√3 meters.

A tree casts a shadow of 20 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?

Using tan(45°) = height / 20, since tan(45°) = 1, we find height = 20 meters.

From a point 50 meters away from a building, the angle of elevation to the top of the building is 60 degrees. What is the height of the building?

Using the formula height = distance * tan(60), height = 50 * √3 ≈ 86.60 meters.

If a man is standing 15 meters away from a tower and sees the top of the tower at an angle of elevation of 30 degrees, what is the height of the tower?

Using tan(30°) = height / 15, we find height = 15 * (1/√3) = 5√3 meters.

A balloon is at a height of h meters. The angles of depression to two points on the ground are 45 degrees and 60 degrees. If the points are 50 meters apart, what is the height of the balloon?

Using the tangent functions: From the first point, h = distance1 * tan(45) and from the second point, h = distance2 * tan(60). Set up the equations to find h.

A hill is 40 meters high. From the top of the hill, the angle of depression to a car on the ground is 30 degrees. How far is the car from the base of the hill?

Using tan(30°) = 40 / distance, we find distance = 40√3 meters.

When observing a tower from a distance of 10 meters, the angle of elevation is 45 degrees. What is the height of the tower?

Using tan(45) = height / 10, we find height = 10 meters.

How do you calculate the width of a river if the angles of depression to both banks from a bridge are known?

Using the formula width = h(cot(angle1) - cot(angle2)) where h is the height of the bridge and angle1 and angle2 are the angles of depression to each bank.

A man is 20 meters from a tree and sees its top at a 60-degree angle of elevation. What is the height of the tree?

Using tan(60) = height / 20, height = 20√3 ≈ 34.64 meters.

A building casts a shadow of 25 meters when the angle of elevation is 30 degrees. What is the height of the building?

Using tan(30) = height / 25, we find height = 25/√3 ≈ 14.43 meters.

If a person observes a plane flying at a height of 1000 meters at an angle of elevation of 45 degrees, how far is the person from the point directly below the plane?

Using tan(45) = height / distance, distance = 1000 meters.