Final answer:
In a right triangle with legs measuring 8cm and 11cm, the hypotenuse measures approximately 13.6cm. The angle x in this triangle is approximately 36.87°.
Step-by-step explanation:
In a right triangle, the two sides are called legs and the hypotenuse. Using the Pythagorean theorem, we can find the length of the hypotenuse (c) by squaring each leg and adding them together: c^2 = a^2 + b^2. In this case, one leg measures 8cm and the other leg measures 11cm. Plugging these values into the formula, we get c^2 = 8^2 + 11^2 = 64 + 121 = 185. Taking the square root of 185, we get c = √185 = 13.6cm.
Now, we can find the angle x using trigonometry. Since we know the lengths of the legs, we can use the sine and cosine functions. The sine of x is equal to the opposite side (8cm) divided by the hypotenuse (13.6cm), so sin(x) = 8/13.6. Taking the inverse sine (sin^-1) of this value, we can find the angle x. Therefore, x ≈ 36.87°.