Question

Based on the given angle measures, which triangle has side length measures that could be correct?

Answer 1

Answer

The triangle in the figure 4 is correct .

Reason

by using the trignometric identity

$tan\theta = \frac{Perpendicular}{Base}$

Thus

$tan 30^{\circ} = \frac{Perpendicular}{Base}$

$tan 30 ^{\circ} =\frac{1}{\sqrt{3}}$

Now in the figure (1)

$tan 30^{\circ} = \frac{13.9}{8}$

$\frac{1}{\sqrt{3}} = \frac{13.9}{8}$

on simplify

$0.5774 \neq 1.7375$

thus side length measures in the figure (1) is not correct .

Now in the figure (2)

$tan30^{\circ} =\frac{16}{8} \\ \frac{1}{\sqrt{3}} =\frac{16}{8} \\ 0.577 \neq 2$

thus side length measures in the figure (2) is not correct .

Now in the figure (3)

$tan 30 ^{\circ} = \frac{8}{16} \\ \frac{1}{\sqrt{3}} =\frac{8}{16} \\ 0.577\neq0.5$

thus side length measures in the figure (3) is not correct .

Now in the figure (4)

$tan30^{\circ} = \frac{8}{13.9} \\ \frac{1}{\sqrt{3}} =\frac{8}{13.9}\\ 0.577 = 0.576(approx)$

 Therefore the figure (4) is correct triangle has side length measures that could be correct

Hence proved

 

Answer 2

Answer:

The answer is D on edgen.

Step-by-step explanation:

D. the 4th figure