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Question

(D) The relation between the Celsius scale temperature $(C)$ and the Fahrenheit scale temperature $(F)$ is given by:$\frac{C}{5} = \frac{F-32}{9}$Rear

Vedclass · Accepted Answer

$\frac{9}{\sqrt{106}}$

Vedclass · Answer

(D) The relation between the Celsius scale temperature $(C)$ and the Fahrenheit scale temperature $(F)$ is given by:$\frac{C}{5} = \frac{F-32}{9}$Rearranging this equation to the form $y = mx + c$ (where $y = C$ and $x = F$):$C = \frac{5}{9}F - \frac{160}{9}$Comparing this with the equation of a straight line $y = mx + c$,the slope of the graph is $m = 	an 	heta = \frac{5}{9}$.Since $	an 	heta = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{5}{9}$,we can consider a right-angled triangle with opposite side $5$ and adjacent side $9$.The hypotenuse is $\sqrt{5^2 + 9^2} = \sqrt{25 + 81} = \sqrt{106}$.Therefore,the cosine of the angle $	heta$ is $\cos 	heta = \frac{	ext{adjacent}}{	ext{hypotenuse}} = \frac{9}{\sqrt{106}}$.

The temperature of a body is measured both in ${ }^{\circ} C$ and ${ }^{\circ} F$. $A$ graph is plotted with ${ }^{\circ} F$ on the $X$-axis and ${ }^{\circ} C$ on the $Y$-axis. Then,the cosine of the angle between the graph and the $X$-axis is

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