Question

Find the value of x.

Answer 1

Answer:

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

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.

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

$cos(60)= \frac{14}{x}$

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

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

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,

$\frac{1}{2} x= 14$

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.

$2* \frac{1}{2} x= 14 *2$

$x=14 *2\\ x=28$

The hypotenuse, x, is equal to 28.