For the given figure, x = 34.640 units.
Step-by-step explanation:
Step 1:
The formulae needed to solve this question are:
[tex]sin\theta = \frac{oppositeside}{hypotenuse} , cos\theta = \frac{adjacentside}{hypotenuse}.[/tex]
The triangle containing x can be split into two right-angled triangles.
So the hypotenuse of the triangle containing the length x and the already given right angle triangle's hypotenuse is the same length.
Step 2:
First, we calculate the hypotenuse of the given triangle.
The angle of the triangle is 45°, the adjacent side's length = 10√3 units. Assume the hypotenuse's length to be a units.
[tex]cos\theta = \frac{adjacentside}{hypotenuse}, cos 45 = 0.707, 0.707 = \frac{10 \sqrt{3}}{a}.[/tex]
[tex]a = \frac{10 \sqrt{3}}{0.707} = 24.498[/tex] units.
Step 3:
For the split triangle, we have the angle as 45°, the opposite side measuring [tex]\frac{x}{2}[/tex] units (only half of x is in each triangle) and the hypotenuse measuring 24.498 units.
[tex]sin\theta = \frac{oppositeside}{hypotenuse} , sin 45 = 0.707, 0.707 = \frac{0.5x}{24.498}.[/tex]
[tex]x= \frac{(0.707)(24.498)}{0.5} = 34.640[/tex]
So x measures 34.640 units.
