y1) A person looks out her window at a building \(50\) feet away. Her angle of depression to the base of the building is \(48^{\circ}\) and her angle of elevation to the top of the building is \(62^{\circ}\).
a) How far is she from the top of the building?
b) How tall is the building?
2) An eagle dropped a fish from its talons \(20\) meters above a lake. The fish dropped at a \(35^{\circ}\) angle. How far did the fish "fly" before it hits the water?
3) Flynn Ryder has arrived to rescue Rapunzel. Rapunzel has let down her hair, but Flynn is a little hesitant about the climb because of the height of the tower. Please help him calculate how long the Rapunzel's hair would have to be for Flynn to climb the tower. He is standing \(12\) feet from the base of the tower and looking up at an \(80^{\circ}\) angle. Flynn is \(5' 10"\)tall and can comfortably reach \(15"\) above his head.
a) How far is she from the top of the building?
b) How tall is the building?
2) An eagle dropped a fish from its talons \(20\) meters above a lake. The fish dropped at a \(35^{\circ}\) angle. How far did the fish "fly" before it hits the water?
3) Flynn Ryder has arrived to rescue Rapunzel. Rapunzel has let down her hair, but Flynn is a little hesitant about the climb because of the height of the tower. Please help him calculate how long the Rapunzel's hair would have to be for Flynn to climb the tower. He is standing \(12\) feet from the base of the tower and looking up at an \(80^{\circ}\) angle. Flynn is \(5' 10"\)tall and can comfortably reach \(15"\) above his head.
5) Yosemite Falls in California has three sections; the Upper Falls, Middle Cascade, and the Lower Falls. From a bridge one half mile away from the falls, the angles of elevation to the top of the Upper Yosemite Falls are \(48.04^{\circ}\) degrees, \(29.70^{\circ}\) degrees to the botton of the Upper Falls, \(17.47^{\circ}\) to the bottom of the Middle Cascade, and \(10.95^{\circ}\) to the bottom of the Lower Falls. Round answers to the nearest foot.
a) What is the elevation of the Upper Falls? b) What is the length of the Upper Falls? c) What is the length of the Middle Cascade? d) What is the length of the Lower Falls? |
6) Two airplanes are flying west towards an airport tower on the same flight path. The planes are flying at altitudes of \(23,000\) ft and \(19,000\) ft and angles of elevations \(5.2^{\circ}\) and \(8.8^{\circ}\). How far is each plane from the tower along the ground in miles? How far apart in the air are the two planes in miles?