The value of x is approximately 25.84 degrees (using sin) or 70.14 degrees (using cos) .
The triangle is a right triangle, with one angle measuring 90 degrees. The other two acute angles are labelled as x and 40 degrees.
We can use the trigonometric ratios sine (sin), cosine (cos), and tangent (tan) to solve for x.
Here are two methods:
Method 1: Using sine (sin)
We know the length of the side opposite the angle x (let's call it a) and the length of the hypotenuse (let's call it c).
We can see from the image that a = 40 and c = 90.
We can use the definition of sin: sin(x) = a/c = 40/90 = 4/9.
Take the inverse sine (arcsin) of both sides to find x: x = arcsin(4/9).
Using a calculator, we get x ≈ 25.84 degrees.
Method 2: Using cosine (cos)
We know the length of the side adjacent to the angle x (let's call it b) and the length of the hypotenuse (c).
We can see from the image that b = 30 and c = 90.
We can use the definition of cos: cos(x) = b/c = 30/90 = 1/3.
Take the inverse cosine (arccos) of both sides to find x: x = arccos(1/3).
Using a calculator, we get x ≈ 70.14 degrees.
Therefore, the value of x is approximately 25.84 degrees (using sin) or 70.14 degrees (using cos).