A lookout post is on top of a hill that is $100 \mathrm{m}$ above sea level. From the base of the lookout post, the angle of depression of a boat out at sea is $30°$, and from the top of the lookout post, the angle of depression of the boat is $60°$. Find the height of the lookout post. [Enter the value excluding units]

A kite string is $48 \mathrm{m}$ long. As the wind blew, the angle between the kite and the ground went from $27$ degrees to $54$ degrees. Determine the increase in the vertical height of the kite above the ground.

Find length $x$ in the following diagram.                [Enter value to the nearest integer]

Find length $x$ in the following diagram. [Enter the value correct up to two decimal places and excluding units]

A $5 \mathrm{m}$ ladder is resting against a vertical wall. The base of the ladder is $2 \mathrm{m}$ from the wall. Keeping its base fixed, the ladder is rotated so that it now rests against the opposite wall which is $1 \mathrm{m}$ away. Determine the angle through which the ladder has been rotated. [Enter the value in degrees excluding degree symbol correct up to one decimal]

A coast guard attendant atop a cliff $120 \mathrm{m}$ high observes two boats in line with him at angles of depression of $45$ degrees and $69$ degrees. Determine how far apart the boats are.