Question

find ( mangle w ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle w=)
submit
work it out

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(x^{2}=y^{2}+z^{2}-2yz\cos X\). In \(\triangle WXY\), let \(y = 11\), \(z = 15\), \(x = 13\). We want to find \(\angle W\), so we use the formula \(x^{2}=y^{2}+z^{2}-2yz\cos W\).
Substitute the values: \(13^{2}=11^{2}+15^{2}-2\times11\times15\times\cos W\).

Step2: Simplify the equation

First, calculate the squares: \(169 = 121+225 - 330\cos W\).
Then, \(169=346 - 330\cos W\).
Rearrange the equation: \(330\cos W=346 - 169\).
\(330\cos W = 177\).

Step3: Solve for \(\cos W\)

\(\cos W=\frac{177}{330}\approx0.5364\).

Step4: Find the angle

\(W=\cos^{-1}(0.5364)\).
Using a calculator, \(W\approx57.5^{\circ}\).

Answer:

\(57.5\)