Calculate the area of a regular octagon inscribed in a unit circle.

In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Calculate the length of the other diagonal.

From the top of an observation post that is 90 meters high, a ranger sights a campsite at an angle of depression of 10°. Turning in a different direction, the ranger sees another campsite at an angle of depression of 13°. The angle between these two sight lines is 35°. How far apart are the campsites?

Two planes leave an airport at the same time, one flying at 300 km/h and the other at 420 km/h. The angle between their flight paths is 75 degrees. After three hours, how far apart are they?

From the top of a building 10 m tall, the angle of elevation to the top of a flagpole is 11 degrees. At the base of the building, the angle of elevation to the top of the flagpole is 39 degrees. Find the height of the flagpole.

In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Find the length of the other diagonal.