Question

question 14 (mandatory) (1 point)
in △abc, a = 6.9 m, b = 15.7 m, and ∠c = 39°. determine c to the nearest tenth of a
metre.
a) 11.2 m
b) 14.5 m
c) 9.9 m
d) 7.3 m
(mandatory) (1 point)
used to determine the length of xin the diagram

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
Substitute \(a = 6.9\), \(b = 15.7\), and \(C = 39^{\circ}\) into the formula:
\(c^{2}=6.9^{2}+15.7^{2}-2\times6.9\times15.7\times\cos(39^{\circ})\)
First, calculate \(6.9^{2}=47.61\), \(15.7^{2}=246.49\), and \(\cos(39^{\circ})\approx0.7771\).
Then \(2\times6.9\times15.7\times0.7771 = 2\times6.9\times15.7\times0.7771\approx169.77\)
\(c^{2}=47.61 + 246.49-169.77\)

Step2: Simplify the expression

\(c^{2}=47.61+246.49 - 169.77=124.33\)
Take the square root of both sides: \(c=\sqrt{124.33}\approx11.2\)

Answer:

a) \(11.2\ m\)