Trigonometry Question

Question

Two hikers start from the common point Y and each heads in a different direction according to the angle shown in the figure. If one hiker camps at point X 560 yards from point Y and the other hiker camps at point Z 539 yards from point Y, what is the distance, to the nearest yard, between the two camps?

Answer 1

Hi Joey.

We don't know the angle from your post, but assume the angle is θ. You can then use the Law of Cosines.

Here's a hint for memorizing the law: It starts with the Pythagorean Theorem (which you've surely memorized): c² = a² + b². This is used to find the length of side c, which is the hypotenuse of the right triangle.

To find the third side, called c, of a non-right triangle is almost the same. If we are given the angle θ which is opposite side c, then we have

c² = a² + b² - 2ab cosine(θ).

Substitute your values and off you go.