Question

Find the value of x.

Answer 1

`\boxed {\boxed {\sf x=28}}`

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.

`cos (\theta) = \frac {adjacent}{hypotenuse}`

`cos(60)= (14)/(x)`

Since we are solving x, we must isolate the variable. First, cross multiply.

`\frac {cos(60)}{1}= (14)/(x)`

Multiply the first numerator (cos60) by the second denominator (x).

Then, multiply the first denominator (1) by the second numerator (14)

`cos (60)*x= 14*1`

`cos(60)*x= 14`

The cosine of 60 is equal to 1/2,

`(1)/(2) x= 14`

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.

`2* (1)/(2) x= 14 *2`

`x=14 *2\\ x=28`

The hypotenuse, x, is equal to 28.