Question

find the length of side a.
c
a
b
a
c
b = 50
c = 48
a = 60°
a = ?

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\).
Substitute \(b = 50\), \(c = 48\), and \(A=60^{\circ}\) (\(\cos60^{\circ}=\frac{1}{2}\)) into the formula:
\(a^{2}=50^{2}+48^{2}-2\times50\times48\times\frac{1}{2}\)

Step2: Calculate each term

• Calculate \(50^{2}=2500\), \(48^{2}=2304\), and \(2\times50\times48\times\frac{1}{2}=2400\)
• Then \(a^{2}=2500 + 2304-2400\)
• \(a^{2}=2404\)

Step3: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{2404}\approx49.0\)

Answer:

\(49.0\)