Question

if the area of the parallelogram below is 143 m², and its height is 11 m, find the length of its base. given triangle ust, find cos t. (round your answer to the nearest hundredth.) select one: a. 13 m b. 17 m c. 11 m d. 9 m

Explanation:

Step1: Recall the cosine - law formula

The cosine - law for a triangle with sides \(a\), \(b\), \(c\) and the angle \(C\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle UST\), let \(u = 13\), \(s = 8\), \(t = 12\), and we want to find \(\cos T\). According to the cosine - law, \(u^{2}=s^{2}+t^{2}-2st\cos T\).

Step2: Rearrange the formula to solve for \(\cos T\)

We can rewrite the formula as \(\cos T=\frac{s^{2}+t^{2}-u^{2}}{2st}\).
Substitute \(s = 8\), \(t = 12\), and \(u = 13\) into the formula:
\[

$$\begin{align*} s^{2}&=8^{2}=64\\ t^{2}&=12^{2}=144\\ u^{2}&=13^{2}=169 \end{align*}$$

\]
Then \(s^{2}+t^{2}-u^{2}=64 + 144-169=39\), and \(2st=2\times8\times12 = 192\).
So \(\cos T=\frac{39}{192}\approx0.20\)

Answer:

\(0.20\)