Answer:
x ≈ 35.5 degrees
Explanation:
To find angle x in the right triangle with sides 13 and 18, we can use trigonometric functions.
label the sides of the triangle as follows:
Opposite side = 13
Adjacent side = 18
Hypotenuse = c (missing side)
We can use the sine function to find angle x:
sin(x) = Opposite / Hypotenuse
sin(x) = 13 / c
To find c (the hypotenuse), use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
c^2 = 13^2 + 18^2
c^2 = 169 + 324
c^2 = 493
c ≈ √493
c ≈ 22.2
Now we can find the value of sin(x):
sin(x) = 13 / c
sin(x) = 13 / 22.2
sin(x) ≈ 0.586
To find angle x, we can use the inverse sine (sin^(-1)) function:
x = sin^(-1)(0.586)
x ≈ 35.5 degrees
Therefore, angle x in the right triangle with sides 13 and 18 is approximately 35.5 degrees.