Answer:
[tex]x=8[/tex]
Step-by-step explanation:
Use the sine ratio because we have the hypotenuse and side opposite the given angle to work with:
[tex]sineX=\frac{opposite}{hypotenuse}[/tex]
Insert the values:
[tex]sin30=\frac{4}{x}[/tex]
Multiply both sides by x:
[tex]x(sin30)=x(\frac{4}{x} )\\\\x*sin30=4[/tex]
Divide both sides by sin30°:
[tex]\frac{x*sin30}{sin30} =\frac{4}{sin30}\\\\x= \frac{4}{sin30}[/tex]
Insert the value of x into a calculator:
[tex]x=8[/tex]
OR:
The little red square means that angle is 90º, and the other given angle is 30°. Since every triangle has a measure of 180°, the other missing angle is 60°. The given triangle is a 30°-60°-90° triangle with the following rules:
[tex]long.leg=short.leg*\sqrt{3}\\\\hypotenuse=short.leg*2[/tex]
The hypotenuse is represented by the variable x. We are given the value of the short leg, which is 4. Solve for the hypotenuse:
[tex]h=4*2\\\\h=8[/tex]
Therefore, the value of x is 8.
:Done
