College Algebra & Trigonometry, 2018a

362 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY
cos 68 ◦ = b 5
Approximating cos 68 ◦ on a calculator:
0.3746 ≈ b 5
5 ∗ 0.3746 ≈ b
1.9 ≈ b
If we use the Pythagorean Theorem with two sides of the triangle to find the
third, then we would say that:
b 2 +4.6 2 =5 2
b 2 +21.16 = 25
b 2 =3.84
b = √ 3.84 ≈ 1.959 ≈ 2.0
The rounding error in this example comes from the fact that the first side we
found was not exactly 4.6. If we wanted a more accurate answer that matches the
answer we found using the cosine ratio, we just need more accuracy in the leg of
the triangle we found.
Calculating 5 ∗ sin 68 ◦ ≈ 4.636 should provide enough accuracy.
b 2 +4.636 2 =5 2
b 2 +21.492496 = 25
b 2 =3.507504
b = √ 3.507504 ≈ 1.8728 ≈ 1.9