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

The bikers will meet at point N, all the questions have been answered below.

What is a Triangle?

A triangle is a polygon with three sides, angles, and vertices.

The triangle MNO is formed on the basis of the data given in the question

If the triangle satisfies the sine-rule then the biker meets the other biker at point N

According to the sine rule

In a Triangle ABC of side length a,b and c respectively

a/ sin A = b/ sin B = c/sin C

NM/sin NOM =21/ sin 61°

NM/sin NOM = 24.01

NO/sin OMN =24/sin 89°

NO/sin OMN = 24.003

∠ONM = ( 180-61-89) = 30°

OM / sin ONM = 12/ sin 30 = 24

• The ratio of the side and angles of the triangle are almost equal, therefore they satisfy the sine rule

        and so, the bikers will meet at point N.

• As they are meeting the distance between them will be zero.

• The measure of the angle between the bikers is as calculated above = 30°.

• The largest angle is opposite to the longer path.

• The triangle formed is an acute angle triangle.

• Total miles they travelled = 24+12+21 = 57 miles.

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