What is the approximate value of x in the diagram below

x = 8 cm

Step-by-step explanation:

The first step in solving this problem is to determine which trig function applies.  The diagram shows that this triangle is a right triangle, that side x is opposite the 25-degree angle, and that the hypotenuse has a length of 18 cm.  

The sine function of an angle Ф is defined as the ratio of the opposite side to the hypotenuse.  In this case, sin Ф (or sin 25 degrees) equals x/(18 cm).

We need to determine the value of x.  Adapt the above equation to this particular situation:  sin 25 degrees = x/(18 cm).

To solve for x, multiply both sides of the most recent equation, above, by (18 cm).  The following results:  (18 cm)(sin 25 degrees) = x.

Next, use a calculator to find the value of sin 25 degrees:  It is 0.4226.

Then the desired value of x is (18 cm)(0.4226), or x = 7.61 cm.  This should be rounded off to x = 8 cm to reflect the level of accuracy of the given 18 cm.