Question

Which is the measure of line segment AB?

A)10 feet
B)15 feet
C)20 feet
D)100 feet

Answer 1

find the last angle:
180-(30+90)
180-(120)
60

Evaluate using sine rule:

`(c)/(sinC)`=
`(b)/(sinB)`

c=
`(bsinC)/(sinB)`

=
`(10sin90°)/(sin30°)`

=20

The length of line segment AB is 20 feet (answer choice C)

Answer 2

AB= 20 feet

Explanation:

Given triangle ABC is a right angle triangle

Use trigonometric ratio to find the length of the Side AB

AB is the hypotenuse

Sin = opposite side divide by hypotenuse

`sin(B)= (AC)/(AB)`

`sin(30)= (10)/(AB)`

Cross multiply it

`sin(30) \cdot AB= 10`

`AB= (10)/(sin(30))`

AB= 20 feet