Question

90+ POINTS PLEASE HELP Choose one problem below and use trigonometry to solve for a missing angle x of the right triangle

Answer 1

`x\approx49.3266\textdegree`

Explanation:

So we want to find Angle x.

Note that we already know the side length of the side opposite to Angle x.

We also know that the hypotenuse is 56.3.

Therefore, we can use the sine function. Recall that:

`\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}`

The opposite side is 42.7. The hypotenuse is 56.3. Substitute:

`\sin(x)=(42.7)/(56.3)`

Take the inverse sine of both sides.

`\sin^(-1)(\sin(x))=\sin^(-1)((42.7)/(56.3))`

The left side cancels:

`x=\sin^(-1)((42.7)/(56.3))`

Use a calculator. Thus:

`x\approx49.3266\textdegree`

And that's our answer :)

Answer 2

`\Huge \boxed{\mathrm{49.33 \° }}`

`\rule[225]{225}{2}`

Explanation:

The triangle is a right triangle.

We can use trig functions to solve for the missing angle.

`\displaystyle \mathrm{sin \theta =(opposite)/(hypotenuse) }`

The opposite side to angle x is 42.7.

The hypotenuse of the right triangle is 56.3.

`\displaystyle \mathrm{sin} (x)=(42.7)/(56.3)`

Taking inverse sin of both sides.

`\displaystyle x=\mathrm{sin^(-1)}( (42.7)/(56.3))`

`x= 49.3265955`

The missing angle measures approximately 49.33°.

`\rule[225]{225}{2}`