A runner starts at point A and runs 860 feet due East to point B.The runner then turns and runs at a bearing of S12E for 175 feet to point C.How far is point C

Question

A runner starts at point A and runs 860 feet due East to point B.The runner then turns and runs at a bearing of S12E for 175 feet to point C.How far is point C form point A.

Answer 1

Ace,

 

You must draw a triangle ABC and label the two given sides. AB = 860 ft and BC = 175 ft. You can calculate angle B as 102°.

 

To find the side AC, you can use the Law of Cosines. Let its length be denoted by b. Then,

 

b² = 860² + 175² −2·860·175·cos 102° ≈ 832806

 

b ≈ √832806 ≈ 912.582

 

Using loose conventions for significant digits, you would round the final answer to 913 feet. (Your textbook or instructor may require only two digits, in which case the correct answer would be 910 ft. This is due to the fact that the bearing was given using an angle of 12° which is taken to have two significant digits.)

 

Let me know if you have any more questions about this before too long.