Question

find the length of side d in the picture, below.
image of a right triangle with angle 60° at the left, hypotenuse 1, and base d
d =
enter your answer in exact form.
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Explanation:

Step1: Identify trigonometric ratio

We have a right - triangle with an angle of \(60^{\circ}\), hypotenuse \( = 1\), and the side \(d\) is adjacent to the \(60^{\circ}\) angle. The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Apply cosine formula

For \(\theta = 60^{\circ}\), \(\cos(60^{\circ})=\frac{d}{1}\). We know that \(\cos(60^{\circ})=\frac{1}{2}\). So, \(d = \cos(60^{\circ})\times1=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)