On a base of 42mm length of the side opposite this angle is 84mm
What angle? What type of figure?
Triangle
To find the length of the side opposite the given angle, we can use the trigonometric function called the sine. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side of the right triangle).
In this case, we're given the length of the adjacent side, which is 42mm. However, we need the length of the hypotenuse to use the sine function.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle.
Let's call the length of the hypotenuse 'c'. Using the Pythagorean theorem, we have:
c^2 = 42^2 + 84^2
c^2 = 1764 + 7056
c^2 = 8820
Taking the square root of both sides, we get:
c ≈ 93.89
So, the length of the hypotenuse is approximately 93.89mm.
Now we can use the sine function to find the length of the side opposite the given angle:
sin(theta) = opposite/hypotenuse
sin(theta) = x/93.89
We don't know the value of the angle, so we can't calculate the sine directly. However, if you have the value of the angle, you can substitute it into the formula above and solve for x.