Question

Pls help me i habe to used sin cos tan to find x but i dont know howTrigonometry

Answer 1

To find x we need to remember the definitions of the trigonometric functions:

`\sin \theta=\frac{\text{opp}}{\text{hyp}}`

`\cos \theta=\frac{\text{adj}}{\text{hyp}}`
`\tan \theta=(opp)/(hyp)`

Now that we have the functions we need to see which thing we need and what things we have.

We know the angle shown is 60°. For that angle we know the hypotenuse; and we need the opposite leg. Then the function we need to use is the one that relates this two sides. From the definitions above we notice that the function we need to use is the sine function. Plugging the values in the definition we have:

`\sin 60=(x)/(8)`

Now we solve the equation for x:

`\begin{gathered} \sin 60=(x)/(8) \\ x=8\sin 60 \\ x=8\cdot\frac{\sqrt[]{3}}{2} \\ x=4\sqrt[]{3} \\ x=6.92 \end{gathered}`

Therefore x is:

`x=4\sqrt[]{3}`

or approximately 6.92.