Question

question in △tuv, u = 750 cm, v = 670 cm and ∠t = 160°. find the length of t, to the nearest centimeter. answer attempt 1 out of 2 score: 1/3 penalty: none submit answer watch video show examples

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for a triangle with sides \(u\), \(v\), \(t\) and the angle \(\angle T\) opposite to side \(t\) is \(t^{2}=u^{2}+v^{2}-2uv\cos T\). Given \(u = 750\) cm, \(v = 670\) cm and \(T=160^{\circ}\), we substitute these values into the formula. So \(t^{2}=750^{2}+670^{2}-2\times750\times670\times\cos(160^{\circ})\).

Step2: Calculate each part

First, \(750^{2}=562500\), \(670^{2}=448900\). And \(\cos(160^{\circ})\approx - 0.9397\). Then \(2\times750\times670\times\cos(160^{\circ})\approx2\times750\times670\times(- 0.9397)=-2\times502500\times0.9397=-946798.5\).

Step3: Calculate \(t^{2}\)

\(t^{2}=562500 + 448900-(-946798.5)=562500+448900 + 946798.5=1958198.5\).

Step4: Find \(t\)

\(t=\sqrt{1958198.5}\approx1399.35\approx1400\) cm.

Answer:

\(1400\) cm