Answer:
[tex]\boxed {\boxed {\sf x=28}}[/tex]
Step-by-step explanation:
This is a right triangle. The small square in the corner represents a 90 degree angle. We can use trigonometry. The three major ratios are:
- sin(θ)=opposite/hypotenuse
- cos(θ)=adjacent/hypotenuse
- tan(θ)= opposite/adjacent
The angle, or θ, is 60 degrees. The side measuring 14 is adjacent to this angle. x is the hypotenuse because it is opposite the right angle. Since we have the adjacent side and the hypotenuse, we use cosine.
[tex]cos (\theta) = \frac {adjacent}{hypotenuse}[/tex]
[tex]cos(60)= \frac{14}{x}[/tex]
Since we are solving x, we must isolate the variable. First, cross multiply.
[tex]\frac {cos(60)}{1}= \frac{14}{x}[/tex]
Multiply the first numerator (cos60) by the second denominator (x).
Then, multiply the first denominator (1) by the second numerator (14)
[tex]cos (60)*x= 14*1[/tex]
[tex]cos(60)*x= 14[/tex]
The cosine of 60 is equal to 1/2,
[tex]\frac{1}{2} x= 14[/tex]
x is being multiplied by 1/2. The inverse of multiplication is division. Divide both sides of the equation by 1/2. Since this is a fraction, you can also multiply by the reciprocal: 2.
[tex]2* \frac{1}{2} x= 14 *2[/tex]
[tex]x=14 *2\\ x=28[/tex]
The hypotenuse, x, is equal to 28.
