1. Find the elevation angle of the sun if a man of 1.75 m. tall, casts a shadow of 82 cm. length on the floor.
2. From a point which is 12 m. soil, an observer obtains a measurement of 53 degrees to the angle of depression of an object found in the soil. About how far is the object point on the ground which is directly under the observer?
3. The string of a comet is taut and forming an angle of 48 degrees with the horizontal. Find the height of the comet with respect the ground, if the line measures 87 m. and the end of the rope is held to 1.3 m. soil.
4. A plane flying at an altitude of 10,000 feet and passes directly over a fixed object on land. A minute later, the depression angle of the object is 42 degrees. Determine the approximate speed of the aircraft.
5. Calculate the width of the street, if an observer on a building, see the other side of it at an angle of 60 degrees from the horizontal.
6. One person is in the window of his apartment which is located at 8m. soil and see the building opposite. Top with an angle of 30 degrees and the bottom at an angle of depression 45 degrees. Determine the height of the building said.
7. A river has two parallel banks. Since the points P and Q from one side, there is a point R on the opposite bank. If the visual form to the address of the bank angle of 40 degrees and 50 degrees respectively, and the distance between points P and Q is 30 meters, determine the width of river.
8. A box is located on a wall so that its lower edge is at a distance of 20 cm. above the eye of an observer situated 2 m from the wall. If the visual angle between the upper and lower edges, respectively, is 10 degrees, what is the height of the picture?
9. A step 6 m. long rests on a vertical wall so that the foot of the ladder is 1.5 m. the base of the wall. What is the angle that the ladder is against the wall and how high the wall reaches the ladder?
10. The lengths of the shadows of two vertical posts are 22 m. and 12 m. respectively. The first pole is 7.5 m. higher than the second. Find the sun's elevation angle and the length of each post.
11. A tree to 12 m. is high on the side of a stream. The angle of elevation of the tree, from a point at 180 m. is 3 degrees. Determine if the stream is above or below the designated point and calculate the level difference.
12. What is the height of a hill, if its elevation angle, taken from its base, is 46 degrees, and taken from a distance of 81 m. is 31 degrees.?
13. On a reef is a beacon whose height is 7.5 m. From a point on the beach can be seen that the angles of elevation to the top and bottom of the lighthouse is 47 degrees and 45 degrees. Calculate the height of the reef.
14. On a horizontal plane, a mast is attached by two wires, so that the straps are on opposite sides. The angles formed by these ties to the ground are 27 degrees and 48 degrees. If the distance enters the wedges is 50 m. How cable has been spent?, what is the height at which the cables are held?
15. From the top of a tower of 200 m. above sea level, the angles of depression of two boats are 47 degrees and 32 degrees respectively. Determine the distance between these boats.
16. A surveyor at C, find two points A and B on opposite sides of a lake. If C is at 5,000 m. of A and 7,500 m. of B and the angle ACB is 35 degrees. What is the width of the lake?
17. Two rangers discovered the same illegal campfire in the direction N 52 ° W and N 55 ยบ E, from their respective positions. The second keeper was 1.93 km. West of the first. If nearest fire warden is the one to go. Which of them has to go and how far to walk?
18. One area is shaped like an isosceles triangle. The base is off a road and has a length of 562 m. Calculate the length of the sides if they form an angle of 23 degrees.
19. A ship leaves a port and travels to the West. At one point rotates 30 degrees North on the West and travel 42 km. further to a point 63 km far. port. How far is the port to the point where he turned the boat?
20. From the top of a tower 300 m. there is a high plane and elevation angle of 15 degrees and a car on the road, on the same side of the plane, with a depression angle of 30 degrees. At the same moment, the car driver sees the plane at an angle of elevation of 65 degrees. If the plane, car, and the observer lie in a vertical plane: calculate the distance between the aircraft and automobiles, also calculate the height at which the plane flies at that time.
21. A triangular area is demarcated by a stone wall of 134 meters, one in front of 205 m. down the road and about 147 m. What angle does the fence with the road?
22. A ladder, whose foot is on the street, forming an angle of 30 degrees with the ground, when its upper end rests on a building on one side of the street, forming an angle of 40 degrees when it meets in a building across the street. If the length of the ladder is 50 m, what is the width of the street?
23. A tree has been broken by the wind so that the two parties are to land a right triangle. The upper part forms a 35 degree angle with the floor, and the distance measured on the ground, from the trunk to the height is 5 m. fall. find the height that was the tree.
24. An observer detects an unidentified flying object statically located at a point space. The observer, using a rangefinder and a sextant, determines that the UFO is at 4460 m. at an elevation angle of 30 degrees. Suddenly the UFO descended vertically to land on the surface. Determine how far the observation point down this object and how far it should go down to touchdown.
25. The angle of one corner of a field in a triangular shape, measures 73 degrees. If the sides, among which is that angle, has a length of 175 feet and 150 feet, determine the length of the third side.
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