Question

Which is the measure of line segment AB? A)10 feet B)15 feet C)20 feet D)100 feet

Answer 1

Answer:

AB= 20 feet

Step-by-step 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

$sin(B)= \frac{AC}{AB}$

$sin(30)= \frac{10}{AB}$

Cross multiply it

$sin(30) \cdot AB= 10$

$AB= \frac{10}{sin(30)}$

AB= 20 feet

Answer 2

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

Evaluate using sine rule:
$\frac{c}{sinC}$=$\frac{b}{sinB}$

c=$\frac{bsinC}{sinB}$

=$\frac{10sin90°}{sin30°}$

=20

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