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

`b = 5 √(3)`

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 = (opp)/(adj)`

`\tan 30^\circ = (5)/(b)`

`b \tan 30^\circ = 5`

`b = (5)/(\tan 30^\circ)`

`b = (5)/((√(3))/(3))`

`b = (15)/(√(3))`

`b = (15 √(3))/(√(3) √(3))`

`b = (15 √(3))/(3)`

`b = 5 √(3)`