Applying the required <em>rule </em>or <em>theorem</em>, it can be concluded that the second biker is <u>farther</u> from the <em>parking lot</em>. The distance of the bikers to the <em>parking lot</em> are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The <u>path</u> of travel of both bikers would form a triangle. Applying the <u>Pythagoras</u> theorem to the path of the <em>first</em> biker would give his <u>distance</u> from the starting point. While applying the <u>cosine</u> rule to the path of <em>second</em> rider would gives his <u>distance</u> to the starting point.
Thus,
a. <u>To determine the distance of the first biker from the parking lot.</u>
Let the required <em>distance </em>be represented by x. Applying the Pythagoras theorem, we have:
=
+
=
+
= 64 + 225
= 289
x =
= 17
x = 17 km
Thus, the <u>first</u> biker is 17.0 km from the <em>starting</em> point.
b. <u>To determine the distance of the second biker from the parking lot.</u>
Let the required <em>distance</em> be represented by x. So that applying the cosine rule, we have:
=
+
- 2ab Cos θ
=
+
- 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
= 289 + 120
= 409
x =
= 20.2237
x = 20.22 km
Thus, the <u>second</u> biker is 20.22 km from the <em>starting</em> point.
Therefore, the second biker is <u>farther</u> from the <em>parking lot</em>.
A sketch of the path of travel for the two bikers is attached for more clarifications.
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