For Each Problem: Sketch a Diagram

Using Trigonometric Ratios

For each problem: Sketch a diagram. Set up an equation. Solve. Round your answers to 4 decimal places. Be sure to include units.

1. A train in the mountains rises 10 feet for every 250 feet it moves along the track. Find the angle of elevation of the track.

2. What is the angle of elevation of the moon if a 7-foot creature that walks in the night casts a shadow 45 feet long?

3. How high is an eruption of Old Faithful if the line of sight from a point 90 feet from the base makes an angle of 57 with the ground? (The sighting instrument is on the ground.)

4. In teeing off, a golfer hooks (to the left) his drive at an angle of 14 from the intended line to the hole. The hole is 150 yards from the tee. If the ball ends up due left of the hole, how far is it from the hole? Draw this diagram from above, looking down upon the situation.

5. A lighthouse built at sea level is 150 feet high. From its top, the angle of depression to a buoy is 25. Find the distance from the buoy to the foot of the lighthouse.

6. To secure a 500 meter radio tower against high winds, guide wires are attached to a ring on the tower. The ring is 5 meters from the top of the tower. The wires form a 15 angle with the tower. Find the distance from the tower’s base to the guide wire’s anchor in the ground.

7. A surveyor is 100 meters from a dam. The angle of elevation to the top of the dam is 26. The surveyor’s instrument is 1.73 meters above the ground. Find the height of the dam.

8. An airplane is approaching the Oakland airport at an altitude of 21000 feet. If you’ve ever flown into Oakland, you know that the airport is at sea level; you barely see land before the wheels hit the ground. The pilot has orders to descend at a constant angle of 6. How far from the runway should the pilot begin the descent?

9. A ladder on a fire truck can be extended to 68 feet when elevated to its maximum angle of 70. The base of the ladder is mounted on the top of the truck which is 7 feet above the ground. How high above the ground will the ladder reach?

10. In a survey for a new highway, an engineer drove two large stakes at points A and B on opposite banks of a river to mark the sites of new bridge abutments. Then, from a point C, 100 feet from B and such that CB  AB, the engineer measured ACB and found it to be 73. What is the width of the river?