Question

What's x ? find the indicated side of the right triangle

Answer 1

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Answer:  $\textsf{x = 6}$

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Given:  $\textsf{The image provided with 2 angles and one side}$

Find:  $\textsf{Solve for the unknown side of x}$

Solution:  In order to determine the length of x we need to use some trigonometric functions.  Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees.  We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin.  Plug in the values and solve for the unknown.

Plug in the values

• $\textsf{sin(30) = }\frac{\textsf{opposite}}{\textsf{hypotenuse}}$

• $\textsf{sin(30) = }\frac{\textsf{3}}{\textsf{x}}$

Multiply both sides by x

• $\textsf{sin(30) * x = }\frac{\textsf{3}}{\textsf{x}}\textsf{ * x}$

• $\textsf{sin(30) * x = 3}$

Divide both sides by sin(30)

• $\textsf{sin(30) * x}*\frac{1}{\textsf{sin(30)}}\textsf{ = 3}}*\frac{1}{\textsf{sin(30)}}$

• $\textsf{x = 3}}*\frac{1}{\textsf{sin(30)}}$

Simplify

• $\textsf{x = 3}}*\frac{1}{\textsf{0.5}}$

• $\textsf{x = 6}$

Therefore, the value of the unknown variable x is 6 units.