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=(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))=(2)/(4)=(1)/(2).`

Answer: 1/2