Question

1. find the length of the indicated side, to the nearest tenth of a metre.5 solution

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is $r^{2}=k^{2}+t^{2}-2kt\cos R$, where $k = 3.6$, $t=4.3$, and $R = 36^{\circ}$.
First, find $\cos(36^{\circ})\approx0.809$.
Then calculate $k^{2}=3.6^{2}=12.96$, $t^{2}=4.3^{2}=18.49$, and $2kt\cos R=2\times3.6\times4.3\times0.809 = 24.99$.

Step2: Substitute values into the formula

$r^{2}=12.96 + 18.49-24.99$.
$r^{2}=12.96+18.49 - 24.99=6.46$.

Step3: Solve for $r$

$r=\sqrt{6.46}\approx 2.5$ m.

Answer:

$2.5$ m