Question

Find the length of side b for the given triangle.
option 1- 5 square root 3 over 3
option 2- 5 square root 3
option 3- 10
option 4- 10 square root 3

Answer 1

Answer:

$b = 5 \sqrt{3}$

Step-by-step explanation:

For the 30-deg angle, 5 is the opposite leg.

b is the adjacent leg.

The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

$\tan A = \dfrac{opp}{adj}$

$\tan 30^\circ = \dfrac{5}{b}$

$b \tan 30^\circ = 5$

$b = \dfrac{5}{\tan 30^\circ}$

$b = \dfrac{5}{\frac{\sqrt{3}}{3}}$

$b = \dfrac{15}{\sqrt{3}}$

$b = \dfrac{15 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

$b = \dfrac{15 \sqrt{3}}{3}$

$b = 5 \sqrt{3}$