Question

question 11 (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) 17°
b) 15°
c) 16°
d) 18°

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 \(a\) 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 \(100 + 144=244\).
The equation becomes \(16=244 - 240\cos C\).
Rearrange it to get \(240\cos C=244 - 16\).
\(240\cos C=228\).
Then \(\cos C=\frac{228}{240}=0.95\).

Step3: Find the angle

Take the inverse - cosine of \(0.95\). \(C=\cos^{-1}(0.95)\).
Using a calculator, \(C\approx18.195^{\circ}\approx18^{\circ}\).

Answer:

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