Question

question 2 (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°
b) 16°
c) 17°
d) 15°

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 10\), \(b = 12\), \(c = 4\). Then \(4^{2}=10^{2}+12^{2}-2\times10\times12\times\cos C\).

Step2: Simplify the equation

\(16=100 + 144-240\cos C\). So \(16=244-240\cos C\). Rearranging gives \(240\cos C=244 - 16=228\). Then \(\cos C=\frac{228}{240}=0.95\).

Step3: Find the angle

\(C=\cos^{-1}(0.95)\approx18^{\circ}\) (using a calculator to find the inverse - cosine value).

Answer:

a) \(18^{\circ}\)