Question

d. For part (c), use the complement of the reference angle to write a different equation. Solve for x to confirm your answer for part (c).

Answer 1

In the given right angled trianged, the hypotenuse side is 6 and the adjacent side is x.

The angle formed by the hypotenuse and the adjacent side is 60 degree

The objective is to find the value of the adjacent side x.

SInce, we are provided with hypotenuse and adjacent, use cosine formula.

`\begin{gathered} \cos \theta=\frac{Adjacent}{\text{Hypotenuse}} \\ \cos 60^0=(x)/(6) \\ \cos (90-30)=(x)/(6) \end{gathered}`

It is known that

`\begin{gathered} \cos (90-\theta)=\sin \theta \\ \cos (90-30)=\sin 30 \end{gathered}`

So,

`\sin 30=(x)/(6)`

From the trignometric table the value of sin 30 is 1/2. Substitute the value in the above equation.

`\begin{gathered} (1)/(2)=(x)/(6) \\ x=(6)/(2) \\ x=3 \end{gathered}`

Hence, the length of the hypotenuse side x is 3.