4.8. Applications of Basic Triangle Trigonometry http://www.ck12.org
- Pythagorean number triples are exceedingly common and should always be recognized in right triangle
problems. Examples of triples are 3, 4, 5 and 5, 12, 13.
Example A
Bearing is how direction is measured at sea. North is 0◦, East is 90◦, South is 180◦and West is 270◦. A ship travels
10 miles at a bearing of 88◦and then turns 90◦to the right to avoid an iceberg for 24 miles. How far is the ship from
its original position?
Solution:First draw a clear sketch.
Next, recognize the right triangle with legs 10 and 24. This is a multiple of the 5, 12, 13 Pythagorean number triple
and so the distancexmust be 26 miles.
Example B
A surveying crew is given the job of verifying the height of a cliff. From pointA, they measure an angle of elevation
to the top of the cliff to beα= 21. 567 ◦. They move 507 meters closer to the cliff and find that the angle to the top
of the cliff is nowβ= 25. 683 ◦. How tall is the cliff?
Note thatαis just the Greek letter alpha and in this case it stands for the number 21. 567 ◦.βis the Greek letter beta
and it stands for the number 25. 683 ◦.
Solution:First, sketch the image and label what you know.
Next, because the height is measured at a right angle with the ground, set up two equations. Remember thatαand
βare just numbers, not variables.