BYU geometry end of course essay assignment

Question

Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. DO NOT use the law of cosines, use your knowledge from the content of this course.

a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.

b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?

c. What is the measure of the angle between the bikers?

d. What is the relationship between the measure of the angles and the paths the bikers took?

e. Classify the triangle the paths created.

f. How many miles did they travel together?

Answer 1

they meet up

30 degree angle between them

It's a 30, 61, 89 triangle, almost a 30-60-90 right triangle

any triangle's angles always sum to 180 degrees

30=180-61-89

the 12 miles is opposite the 30 degree angle

the 21 miles is opposite the 61 degree angle

the 24 miles is opposite the 89 degree angle, almost the hypotenuse of a right triangle.

the larger the angle, the larger the opposite side

21 miles is about 24sqr3/2 = 12sqr3 = about 12(1.732) = about 20.784 miles

If A goes faster, it's possible they even arrive at the very same time together.

A goes a total 12+21 = 33 miles to meet up with B who went 24 miles

if A goes 16.5 mph and B goes 12 miles per hour, then they meet together

at the same time, in 2 hours