Question

question 8 (1 point)
what is the length of the pond to the nearest tenth of a metre?
22.4 m
28°
18.5 m
11.4 m
9.5 m
10.6 m
10.0 m

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). Let \(a = 18.5\), \(b=22.4\) and \(\theta = 28^{\circ}\). First, find \(\cos(28^{\circ})\approx0.8829\).

Step2: Calculate \(c^{2}\)

$$
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$$

Step3: Find \(c\)

\(c=\sqrt{106.04}\approx 10.3\approx10.0\) (rounded to the nearest tenth)

Answer:

10.0 m