Section 1.20 - Sample problem: trigonometry



		What is the length of side b of this triangle? What is θ in degrees? in radians?

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

Variables

	short leg	a = 8.16 m
	long leg	b
	hypotenuse	c = 17.2 m
	angle	θ

What is the strategy?

Use the Pythagorean theorem to calculate the length of the third side.
Calculate the cosine of θ and then use the arccosine function on a calculator (or consult a table) to determine θ in degrees.
Convert θ to radians.

Mathematics principles

c² = a² + b²

cos θ = adjacent/hypotenuse

360° = 2π rad

Step-by-step solution

There are other ways to solve this problem. For example, you could first find θ using the arccosine function, and then use the tangent ratio to find the length of the third side.