Question

On a circle, a line is drawn from the origin to A(5, 12). The angle θ

is between the line and the x-axis. A student argues that the Pythagorean Theorem can be used to find cosθ
. Identify the strategy that supports the student's

Answer 1

B. Use the squares of 5 and 12 to find the length of the hypotenuse

Explanation:

You want a strategy for finding the cosine of the angle θ between the +x axis and its terminal ray from the origin through point A(5, 12).

Cosine

The cosine is the ratio of the x-coordinate of the point to its distance from the origin. The distance of the point from the origin can be found by making use of the Pythagorean theorem.

h² = x² + y²

h² = 5² + 12²

Finding the length of the hypotenuse makes use of the squares of 5 and 12.

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Additional comment

To finish the calculation, ...

h = √(25 +144) = √169 = 13

cos(θ) = x/h = 5/13

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