Question

find x.
write your answer as an integer or as a decimal rounded to the nearest tenth.
x =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). In \(\triangle VWX\), let \(a = x\), \(b = 6\), \(c = 10\), and \(A=64^{\circ}\). Then \(x^{2}=6^{2}+10^{2}-2\times6\times10\times\cos64^{\circ}\).

Step2: Calculate each term

First, \(6^{2}=36\), \(10^{2} = 100\), and \(2\times6\times10 = 120\). \(\cos64^{\circ}\approx0.4384\). So \(x^{2}=36 + 100-120\times0.4384\).

Step3: Simplify the right - hand side

\(x^{2}=136-52.608\). Then \(x^{2}=83.392\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{83.392}\approx9.1\).

Answer:

\(x = 9.1\)