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 \(c^{2}\)

\[

$$\begin{align*} c^{2}&=18.5^{2}+22.4^{2}-2\times18.5\times22.4\times0.8829\\ &=342.25 + 501.76-2\times18.5\times22.4\times0.8829\\ &=342.25+501.76-(79.2\times22.4\times0.8829)\\ &=342.25 + 501.76-(1774.08\times0.8829)\\ &=342.25+501.76 - 1565.24\\ &=844.01-1565.24\\ &=106.04 \end{align*}$$

\]

Step3: Find \(c\)

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

Answer:

10.0 m