32. Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answer to the nearest whole number.

18cm and 7m

Step-by-step explanation:

Since these are right triangles, you can use the SOH, CAH, TOA equations to solve for the unknown sides.  Most people remember these by remembering SO CA TOA which sounds like you're saying SUCK A TOA.  The opposite and adjacent are the sides either opposite or adjacent to the angle you know.

SOH= Sin of angle = opposite over hypotenuse

CAH= Cos of angle = adjacent over hypotenuse

TOA= Tan of angle = opposite over adjacent

Triangle 1:  You have to use TOA since you know the angle and the adjacent side to the angle and you are looking for the opposite side from the angle.

                         side a

Tan 61 deg =  simplifying you get    Side a = (tan 61 deg) x 10cm

                          b=10cm

Answer rounded to nearest whole number is 18cm

Traingle 2:  Based on the given angle, you are looking for the opposite side and you know the hypotenuse.  So you can use SOH or the sin of the angle is equal to the opposite over the hypotenuse.

                       side a

Sin 34 deg =  simplifying you get    Side a = (sin 34 deg) x 13m

                        13 m

Answer rounded to nearest whole number is 7 m