How long of a ladder is needed to reach a windowsill 50 feet above the ground if the ladder rests against the building making an angle of 75∘ with the ground?

From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the plane descends in a straight line to the runway. Determine the angle of descent (in degrees) of the plane.

Draw an angle in standard position whose terminal side contains the point (3, –2). Find the distance from the origin to this point.

Two of the sides of an isosceles triangle have lengths of 10cm and 4cm. Which length must be the length of the base?

At a point 65 feet from the base of a church, the angles of elevation to the bottom of the steeple and the top of the steeple are 35 and 43, respectively. Find the height of the steeple.

A jogger runs along two sides of an open rectangular lot. If the first side of the lot is 200 ft long and the diagonal distance across the lot is 400 ft, what is the measure of the angle formed by the 200-ft and 400-ft dimensions? To the nearest foot, how much farther does the jogger run by travelling the two sides of the block rather than the diagonal distance across the lot?