Question

question 15 (mandatory) (1 point)
a woman has a triangular garden with side lengths of 10 m, 12 m, and 4 m.
determine the angle between the side lengths of 10 m and 12 m to the nearest
degree.
a) ( 18^{circ} )
b) ( 16^{circ} )
c) ( 17^{circ} )
d) ( 15^{circ} )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 10\), \(b = 12\), and \(c = 4\). We want to find the angle \(C\) between sides \(a\) and \(b\).
Substitute the values into the formula: \(4^{2}=10^{2}+12^{2}-2\times10\times12\times\cos C\).
So, \(16 = 100 + 144-240\cos C\).

Step2: Simplify the equation

First, calculate \(100 + 144=244\). Then the equation becomes \(16=244 - 240\cos C\).
Rearrange it to get \(240\cos C=244 - 16\).
\(240\cos C=228\).

Step3: Solve for \(\cos C\)

\(\cos C=\frac{228}{240}=0.95\).

Step4: Find the angle \(C\)

Take the inverse - cosine of \(0.95\), \(C=\cos^{-1}(0.95)\approx18^{\circ}\).

Answer:

A. \(18^{\circ}\)