The value of x is 4.655cm.
1. Identify the relevant triangles and sides:
We have two right-angled triangles in the diagram. Let's call the one on the left with the 38-degree angle triangle A and the one on the right with the 90-degree angle triangle B.
In triangle A, we are given the length of a side (5.9587 cm) adjacent to the 38-degree angle and need to find the length of the opposite side (x).
2. Use the tangent function:
Since we have an adjacent side and need to solve for the opposite side in a right-angled triangle, we can use the tangent function (tan).
The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side (opposite/adjacent).
3. Apply the formula to triangle A:
For triangle A, we can write the equation as: tan(38°) = x / 5.9587 cm
4. Solve for x:
To find x, we can rearrange the equation to isolate it: x = tan(38°) * 5.9587 cm
Using a calculator, we can find that tan(38°) ≈ 0.7854.
Substituting this value, we get: x = 0.7854 * 5.9587 cm ≈ 4.655 cm
Therefore, the value of x is approximately 4.655 cm.