1) A lighthouse stands at the top of a vertical cliff. A boatman \(290\) meters off shore finds that the angles of elevation to the top and bottom of the light house are \(28^{\circ}\) and \(24^{\circ}\) respectively. How tall is the lighthouse to the nearest tenth? Start by drawing and labeling the diagram.
2) Solve the right triangle. Round angles to the nearest degree and leave lengths in simplified radical form, where possible.
2) Solve the right triangle. Round angles to the nearest degree and leave lengths in simplified radical form, where possible.
3) The terminal side of an angle, \(\theta\), in standard position passes through point \(\left(5,-3\right)\). Find the six trigonometric ratios for this angle. Write your answers as rationalized fractions, where appropriate.
4) An airplane is at an altitude of \(33,000\) ft. when the pilot starts the descent to the airport. The pilot needs the angle of depression of the plane to be at an angle of \(3^{\circ}\). How many miles away from the airport must the descent begin, to the nearest mile?
5) Find the perimeter of the triangle to the nearest unit.
6) When Vertical Endeavors, a rock climbing gym in Glendale Heights Illinois opened in 2014, it became the largest indoor rock climbing gym in the United States with 45,000 square feet of climbing surface. A person visits this impressive gym and wants to know how tall the wall is. They stand \(10\) feet away from the wall and measure the angle of depression to the bottom of the wall at \(29.2^\circ\) and observes the angle of elevation to the top of the wall to be \(68.9^\circ\). Given this information, how tall is the wall at Vertical Endeavors?
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