Question

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Answer 1

Answer:

C)

Step-by-step explanation:

in order to understand which triangle would lie on the given line we should figure out the slope of the given line first

remember that,

$\displaystyle m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}}$

from the graph let's take two points where the line passes i.e (0,0) and (4,6)

substitute:

$\displaystyle m = \frac{6- 0}{ 4 - 0}$

simplify substraction:

$\displaystyle m = \frac{6 }{ 4 }$

reduce fraction:

$\displaystyle m = \frac{3}{ 2}$

now we need a triangle which tan ratio equal to the slope in that case we can consider the third triangle

$\displaystyle \tan( \theta) = \frac{30}{20}$

reduce fraction:

$\displaystyle \tan( \theta) = \frac{3}{2}$

since the tan ratio of the third triangle equal to the slope of the line

hence, our answer is c