# 10 Trigonometry Application Word Problems : Angles and Lengths

1. Suppose that a boat leaves Jacksonville traveling at a bearing of 110o. It goes 30.0 km, and then travels 100.0 km at a bearing of 170o. How far is it from Jacksonville?

2. Suppose that I am trying to judge the distance across a lake. I stand facing some house on the opposite shore. I turn 95o to the left, and walk 20 meters. Now the angle between the house and my original position is 70o. How far is the house from my original position?

3. What is the angular velocity of the minute hand on a clock?

4. Suppose a rope is tied to a pulley with a radius of 1 meter. The pulley rotates 5 times a minute. What is the angular velocity of the pulley and the linear velocity of the rope?

5. Consider the triangle with vertices at (6,5), (-4,2), and (0,0). Find the lengths of each side and the measures of each angle.

6. Suppose that I build a ramp that to a platform that is 6 meters high. If the ramp is 3 meters long, what is the angle of inclination?

7. Suppose that I lean my ladder against a wall. If the ladder is 4 meters long, and the base is 2 feet from the wall, how high up the wall does the ladder reach?

8. Suppose a wheel with a radius of 0.5 meters rolls down a track at 3.5 meters per second. How many times does the wheel rotate per second?

9. Suppose a wheel with a radius of 0.4 meters rolls down a 40 meter track. How many times does the wheel spin until it reaches the end of the track?

10. Consider the following diagram. Find the length of y. Express as a sum of radicals.

Please see the attached file for the fully formatted problems.

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Ten trigonometry word problems are solved. The solution is detailed and well presented. Helpful diagrams are included.