Question

Solve for x in the triangle...

Answer 1

tan = opposite/adjacent

tan 36° = $\frac{x}{11}$

Cross multiply.

x = 0.726542528 * 11

x = 7.99196781

x = 8.0 (rounded to nearest tenth).

Answer 2

Here we have a relatively basic trigonometry problem using a right triangle. 

We are looking to calculate the value of the side OPPOSITE to our given angle of 36 degrees. We are given the length of the side ADJACENT to this angle. Using this knowledge, we must first determine what trigonometric ratio we need to use. 

For the purpose of answering this question, I will label the angle of 36 degrees angle A.

Because of the values we have been given, the best ratio to use would be:

sin(A) = opposite/hypotenuse

So, if we plug in our known and unknown values, we end up with:
sin(36) = x / 11

To find x, we must first try and get x on one side of the equation, so I am going to do that by multiplying both sides by 11, giving us this equation:

11 × sin(36) = x

Next, multiply (( 11 × sin(36) )), and this will give you the value the length of side X. 

So, your answer should end up as 6.5 if we round the decimal.