Elevation of an Angle

Question

Two straight roads diverge at an angle of 35°. Two cars leave the intersection at 2:00 P.M., one traveling at 50 mi/h and the other at 58 mi/h. How far apart are the cars at 2:30 P.M.? (Round your answer to two decimal places.)

Answer 1

Hi Michelda,

 

First you get the distance each traveled by using the formula: distance=speed*time

 

Call them distance a and b. And call the other one c. See how they form a triangle and call the angle between the two C.

 

Then because you now have two known sides and the angle between them you use the cosine formula.

 

c² = a² + b²- 2ab(cos C)

 

c² = (50*0.5)² + (58*0.5)² -2*(50*0.5)(58*0.5)cos(35⁰ )

 

hope this helps

 

Answer 2

Draw a triangle with an angle of measure 35°.  Since 

distance = (rate)(time), one side of the angle has length

(50mph)(0.5 hours) = 25 miles, while the other side of the angle has length (58mph)(0.5 miles) = 29 miles. 

 

Now, let x = distance between the cars after 0.5 hours

                = length of the third side of the triangle

 

by the Law of Cosines, x² = 25² + 29² -2(25)(29)cos35°

                                        = 625 + 841 - 1187.7705

                                        = 278.2295

                                   x = √(278.2295) ≈16.68 miles