The area of the base of a regular hexagonal pyramid is and the lateral edge is two times the length of the base edge (see the picture). Find the volume of the pyramid.
The base of a right pyramid is a regular hexagon of side and its slant surfaces are inclined to the horizontal at an angle of (see the picture). Find the volume.
A plane is flying at a speed of and according to the compass the axis of the airplane is still heading westbound. What angle will the flight path of the airplane make with the east-west direction if the south wind starts to blow at a speed of ? Round the result to two decimal places.
The distance between the places and on a straight road is . There is a balloon above the road between the places and . See the picture. The angles of elevation from the places and to the balloon are and respectively. What is the height of the balloon?
Calculate the height between two floors if you know that the number of stairs between the floors is , the slope of the staircase is and the depth of a stair is .
From the highest window of Orava Castle, the angles of depression to the banks of the Orava river are and . The height of the window above the river is . What is the width of the river?
An observer was watching an approaching plane flying at a height of in a straight line with constant velocity. At the first moment of measurement the observer saw the plane to be at an angle of elevation of . After seconds the angle of elevation changed to . What was the speed of the plane? Round the result to ones.
What is the width of a computer screen if the ratio of its width and height is and the computer has -inch monitor? Round the result to two decimal places. ( inch=)