Question

Please help!!!! I need to pass this class!!

Answer 1

Answer:

x is approximately 69.39 degrees.

Step-by-step explanation:

To find x in this triangle, we can use the sin rule:

$\frac{a}{sin(A)} =\frac{b}{sin(B)}$

The corresponding angle for each length is the one that lies directly opposite it. E.g. if 3.5 was our length 'a', then 55 degrees would be our angle A.

So let's take 3.5 and 55degrees as our length and Angle A, and 4 and x degrees as our length and angle B as we are trying to solve for x.

This would give us the following equation:

$\frac{3.5}{sin(55)} =\frac{4}{sin(x)}$

Since we are solving for an angle, it will be easier to rearrange the equation if we have it as the numerator, so we can flip the fractions to make it easier. It will still be equal as we are looking for the ratio.

$\frac{sin(55)}{3.5} =\frac{sin(x)}{4}$

From here let's isolate the sin(x) by multiplying by 4 and solving the values we have so far:

$\frac{4 sin(55)}{3.5} =sin(x)\\\frac{3.2766}{3.5} =sin(x)\\0.936=sin(x)$

Now the final step is to use inverse sin to cancel the sin so we just have x:

$sin^{-1} 0.936=x\\x=69.39$

x is approximately 69.39 degrees.

Hope this helped!