Final answer:
To determine the size of angle x in the right-angled triangle with sides 14 cm and 17.5 cm, use the tangent trigonometric ratio. Calculate the inverse tangent of 14 divided by 17.5 to find x in degrees.
Step-by-step explanation:
The question involves using trigonometric ratios to calculate the size of an angle in a right-angled triangle. Since we have the lengths of the sides of a right-angled triangle, 14 cm and 17.5 cm, and need to find the angle x, we can use trigonometry. To find the angle x, we can use the trigonometric ratio known as the tangent (tan), which is the ratio of the opposite side to the adjacent side in a right-angled triangle. The formula we would use is:
tan(x) = opposite/adjacent
Substituting the given lengths (opposite = 14 cm, adjacent = 17.5 cm), we get:
tan(x) = 14 / 17.5
To find the angle x, we take the inverse tangent (arctan or tan-1) of the ratio:
x = tan-1(14 / 17.5)
Using a calculator, we find that x is approximately equal to the nearest degree, which will be our answer.