Find the value of x rounded to the nearest tenth. The diagram is not drawn to scale. The adjacent is 12cm wide and the angle of the hypotenuse is at 35 degrees.

To find the value of x in this right triangle, we can use the cosine function, which relates the adjacent side to the hypotenuse. According to trigonometric principles:

cos(θ) = adjacent / hypotenuse

Here, θ is 35 degrees, and the length of the adjacent side is 12 cm. We need to find hypotenuse (x).

Rearranging the formula to solve for the hypotenuse:

hypotenuse = adjacent / cos(θ)

Substituting the known values:

x = 12 / cos(35°)

Using a calculator to find cos(35°), we get approximately 0.8192. Now plug this back into the equation:

x ≈ 12 / 0.8192

This simplifies to:

x ≈ 14.65 cm

Rounding x to the nearest tenth gives us:

x ≈ 14.7 cm

Therefore, the value of x is approximately 14.7 cm.