Question

fall 2025 geometry b wwva right triangle relationships and trigonometry the law of cosines is used to find the value of m. m² = 27²+18² - 2(27)(18)cos(25°) m²≈729 + 324-(972)cos(25°) m²≈1053-(972)cos(25°) to the nearest whole number, what is the value of m? 43 13 45 14

Explanation:

Step1: Calculate the right - hand side of the law of cosines formula

First, calculate \(27^{2}=729\), \(18^{2} = 324\), and \(2\times27\times18=972\). So the right - hand side of the formula \(m^{2}=27^{2}+18^{2}-2(27)(18)\cos(28^{\circ})\) is \(729 + 324-972\cos(28^{\circ})\). We know that \(\cos(28^{\circ})\approx0.8829\). Then \(972\cos(28^{\circ})\approx972\times0.8829 = 858.1788\), and \(729+324 - 858.1788=194.8212\).

Step2: Find the value of \(m\)

Since \(m^{2}\approx194.8212\), then \(m=\sqrt{194.8212}\approx13.96\approx14\).

Answer:

14