Answer:
part a: AB = 12cm
part b: AB = 18cm
Explanation:
sin(angle)=OPP/HYP
sine of an angle is a ratio of two sides of a right triangle. For sine, the ratio is the opposite side over the hypotenuse. In part a the marked angle is 30° and AB is the opposite side. The hypotenuse is given, 24cm.
So the sin 30°
= opp/hyp
= AB / 24
also given is the fact that sin30°=.5
Substitute that into our equation also.
sin30° = AB/24
.5 = AB/24
multiply both sides by 24.
.5×24 = AB
12 = AB
AB is 12 cm.
Part b is an identical calculation except the hypotenuse is 36cm.
sin30° = AB/36
.5 = AB/36
.5×36 = AB
18 = AB
AB is 18cm.
They may be trying to lead you to discover some shortcut patterns in a 30°-60°-90° triangle. That is that the short leg is HALF the hypotenuse OR the hypotenuse is double the short leg.