Question

find w.

write your answer as an integer or as a decimal rounded to the nearest tenth.

w =
submit

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( w^{2}=y^{2}+x^{2}-2yx\cos W\). Here, \(y = 12\), \(x = 11\), and \(W=11^{\circ}\).
Substitute the values: \(w^{2}=12^{2}+11^{2}-2\times12\times11\times\cos(11^{\circ})\).

Step2: Calculate each term

First, \(12^{2}=144\), \(11^{2}=121\).
\(\cos(11^{\circ})\approx0.9816\).
\(2\times12\times11\times\cos(11^{\circ}) = 264\times0.9816=259.1424\).
Then \(w^{2}=144 + 121-259.1424\).
\(w^{2}=265-259.1424 = 5.8576\).

Step3: Find \(w\)

Take the square - root of \(w^{2}\), \(w=\sqrt{5.8576}\approx2.4\).

Answer:

\(2.4\)