in \\(\\triangle tuv\\), \\(u = 750\\) cm, \\(v = 670\\) cm and \\(\\angle t = 160^\\circ\\). find the…
in \\(\\triangle tuv\\), \\(u = 750\\) cm, \\(v = 670\\) cm and \\(\\angle t = 160^\\circ\\). find the length of \\(t\\), to the nearest centimeter. \nanswer attempt 1 out of 3
Answer
Explanation:
Step1: Apply Law of Cosines
$$t^2 = u^2 + v^2 - 2uv\cos(T)$$
Step2: Substitute given values
$$t^2 = 750^2 + 670^2 - 2(750)(670)\cos(160^\circ)$$
Step3: Calculate each term
$750^2 = 562500$, $670^2 = 448900$, $2(750)(670)=997500$, $\cos(160^\circ)\approx-0.9397$ $$t^2 = 562500 + 448900 - 997500(-0.9397)$$
Step4: Simplify the expression
$$t^2 = 1011400 + 937350.75 = 1948750.75$$
Step5: Solve for t
$$t = \sqrt{1948750.75} \approx 1396$$
Answer:
1396