Conceptual Physics

1.14 - Sample problem: trigonometry

The lengths of two sides of a right triangle are shown.

Variables

What is the strategy?

1. Use the Pythagorean theorem to calculate the length of the third side.


2. Calculate the cosine of ș and then use the arccosine function on a calculator (or consult a table) to determine ș in degrees.


3. Convert ș to radians.

Mathematics principles

c^2 = a^2 + b^2

cosș = adjacent/hypotenuse

360° = 2ʌ rad

Step-by-step solution

First we use the Pythagorean theorem to find the length of the longer leg.

Now, we use the lengths of the sides to find the value of the cosine of ș, and then look up the arccosine of this ratio.

What is the length of side b of this

triangle?

What is ș in degrees? in radians?

short leg a = 8.16 m

long leg b

hypotenuse c = 17.2 m

angle ș

Step Reason

1. c^2 = a^2 + b^2 Pythagorean theorem

2. (17.2 m)^2 = (8.16 m)^2 + b^2 enter values

3. b^2 = 17.2^2 – 8.16^2 = 229 solve for b^2

4. b = 15.1 m take square root

Step Reason

5. cos ș = adjacent/hypotenuse definition of cosine

6. cos ș = (8.16 m)/(17.2 m) enter values

7. cos ș = 0.474 divide

8. ș = arccos(0.474) definition of arccosine

9. ș = 61.7° use calculator

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