A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 940 ft out in the plain from the base of the mountain. Find the shortest length of cable needed. (Round your answer to the nearest foot.) The shortest length of the cable needed is ft.

A pedestal is 5.43 feet tall, and a statue is placed on top of it. A spotlight on the floor lights up the pedestal and statue. [a] The angle of elevation from the spotlight to the bottom of the statue is 57 degrees , and the angle of depression from the top of the statue to the spotlight is 71 degrees .How tall is the statue ?Your final answer must be an exact value (ie. do not use your calculator).Your final answer may involve fractions, radicals, angles and/or trigonometric functions and the decimal number given in the problem. HINT: You will need to calculate another quantity first. [b]Using your calculator, round the answer to [a] to 2 decimal places. [c] The pedestal is replaced with a pedestal of a different height, with the same statue placed on top of it.The spotlight is moved and tilted so that the angle of elevation from the spotlight to the bottom of the statue is now 41 degrees , and the angle of depression from the top of the statue to the spotlight is now 64 degrees…

It is desired to determine the height of a flagpole. Assuming that the ground is level, an instrument is set up 352.77 feet from the flagpole with its telescope centered 5.07 feet above the ground. The telescope is sighted horizontally to a point 5.07 feet from the bottom of the flagpole and then the angle at the instrument looking to the top of the pole is measured. That angle is 23 degrees 3 minutes. How tall is the flagpole from its base? Give your answer to two decimal places with NO units.

How far does the tip of a 1.39 m pendulum travel as it swings through an angle of 6.3°? The distance through which the end of the pendulum swings is m. (Simplify your answer. Round to three decimal places as needed.)