Question

Use a 30 - 60 - 90 triangle to find the cosine of 60 degrees

Answer 1

1) To build a 30-60-90 triangle, we start with an equilateral triangle with sides of length 4:

2) Now, we split the triangle with a vertical line:

3) From trigonometry, we know that:

$\cos \theta=\frac{AC}{H}\text{.}$

Where:

• θ is the angle of interest,

,

• AC is the adjacent cathetus to the angle θ,

,

• H is the hypotenuse.

In this case, we have:

• θ = 60°,

,

• AC = 2,

,

• H = 4.

Replacing these data in the formula above, we get:

$\cos (60^{\circ})=\frac{2}{4}=\frac{1}{2}.$

Answer: 1/2