A man is standing on the street outside of a tall building. A girl is standing at a window up on the third floor of the building. Here are two facts about the situation:

1.  The angle from the man on the street up to the girl in the window is 60°.

2.  The horizontal distance from the man on the street to the point directly underneath the girl is 5,2 m.

Calculate the vertical distance from the girl to the point directly below her.

A person stands at Point A. They look up at a bird sitting on the top of a tree (at Point B).

The height of the tree is 9 m, the line-of-sight distance from Point A to the top of the tree (Point B) is 10,39 m and the angle of inclination (from the horizontal) to the top of the tree is .

Match the steps and reasons below to prove that is a parallelogram.

The escalator at the mall slopes at an angle of 30° and is 20 m long.

Through what height would a person be lifted by travelling on the escalator? (Round your answer to two decimal places, without units. Use "," and NOT "." as a decimal point)

Calculate the coordinates of the midpoint  between point  and point  correct to 1 decimal place.

What is the equation of the line that contains the points  and 

Write it in the form of

A line is drawn perpendicular to . It passes through the point (4; 0).

What is the new equation in the form of 

Points and  are points on the same line.

You are given the following diagram:

You are also told that line  has a gradient  of 2. Calculate the missing coordinate of point .

You are given the following diagram:

Calculate the equation of the line .