Question

Pls help me with questions 13 directions find the value of x round your answer to the nearest tenth

Answer 1

x = 24.2

y = 12.1

Step-by-step explanation:

The side with length x, the side with length 21, and the angle of 60° are related by the trigonometric function sine, so:

`\begin{gathered} \sin 60=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin 60=(21)/(x) \end{gathered}`

Therefore, solving for x, we get:

`\begin{gathered} x\cdot\sin 60=x\cdot(21)/(x) \\ x\cdot\sin 60=21 \\ (x\cdot\sin60)/(\sin60)=(21)/(\sin 60) \\ x=(21)/(\sin 60) \end{gathered}`

Then, sin 60 = 0.86, so the value of x is:

`\begin{gathered} x=(21)/(0.86) \\ x=24.2 \end{gathered}`

In the same way, the value of y is related by the trigonometric function tangent as:

`\begin{gathered} \tan 60=(Opposite)/(Adjacent) \\ \tan 60=(21)/(y) \end{gathered}`

So, solving for y, we get:

`\begin{gathered} y\cdot\tan 60=y\cdot(21)/(y) \\ y\cdot\tan 60=21 \\ (y\cdot\tan60)/(\tan60)=(21)/(\tan 60) \\ y=(21)/(\tan 60) \end{gathered}`

Since tan 60 = 1.73, we get:

`y=(21)/(1.73)=12.1`

Therefore, the answers are:

x = 24.2

y = 12.1