Question

I need to know how to do this one.​

Answer 1

Answer:

$x \approx 11.6906$

I made the assumption those were right triangles.

Step-by-step explanation:

I like your 30 there.

I found the length in orange by doing 55-30=25.

Now we can try to find the length in light purple by doing orange length plus the length you found which is 25+30=55.

So we can use a trig function to find $x$.

I made another picture to focus our problem more.

Now if you look at the triangle we have here and refer to trig right triangle definitions, we can setup an equation form this.

The opposite side of the angle, whose measurement is $12$ degrees, is $x$.

The adjacent side of the angle, whose measurement is $12$ degrees, is $55$.

So I will use the tangent ratio.

$\tan(12^\circ)=\frac{\text{opposite}}{\text{adjacent}}$

$\tan(12^\circ)=\frac{x}{55}$

Multiply both sides by 55:

$55 \cdot \tan(12^\circ)=x$

Now it is handy dandy calculator punching in time:

$11.6906 \approx x$

$x \approx 11.6906$