Idiot\'s Guides Basic Math and Pre-Algebra

242 Part 3: The Shape of the World

CHECK POINT

Tr ia n g le ABC has a right angle at ’B. AB = 12 cm, BC = 5 cm and AC = 13 cm. Find

each trig ratio.

21. sin ’A


22. tan ’B


23. cos ’A
    24. tan ’A
    25. sin ’B

Finding Missing Sides

With these three ratios and a table of their values (or a calculator that has keys for them), it is

possible to solve for any unknown side of the right triangle if another side and an acute angle are

known, or to find the angle if two sides are known.

MATH IN THE PAST

Once upon a time, students had to rely on tables to look up the values of the ratios for

each family of right triangles, but now the sine, cosine, and tangent of an angle can be

found with a few keystrokes on your calculator. Because the other three ratios don’t

have keys on the calculator, they’re not used as often.

In right triangle 'ABC, hypotenuse AC is 6 cm long, and ’A measures 32r. To find the length of

the shorter leg, it helps to first make a sketch to help you visualize the triangle. The shorter leg

will be opposite the smaller angle, so if you draw the triangle and calculate the measure of each

angle, you’ll see that m’A = 32r, m’B = 90r, and m’C = 58r. You need to find the side opposite

the 32r angle, or side BC.

You need a ratio that talks about the opposite side and the hypotenuse (because that’s the side

you know). The sine is the one you want. sin(32 )

6

BC

AC

x

55. From your calculator, you can find

that sin(32^ )≈0.5, so 0.53

6

x and x≈3.2. The side opposite the 32r angle is about 3.2 cm.

A B

C

32°

6