Question

BONUS: Find x. 15) 10V3

Answer 1

For the given figure, x = 34.640 units.

Step-by-step explanation:

Step 1:

The formulae needed to solve this question are:

$sin\theta = \frac{oppositeside}{hypotenuse} , cos\theta = \frac{adjacentside}{hypotenuse}.$

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.

$cos\theta = \frac{adjacentside}{hypotenuse}, cos 45 = 0.707, 0.707 = \frac{10 \sqrt{3}}{a}.$

$a = \frac{10 \sqrt{3}}{0.707} = 24.498$ units.

Step 3:

For the split triangle, we have the angle as 45°, the opposite side measuring $\frac{x}{2}$ units (only half of x is in each triangle) and the hypotenuse measuring 24.498 units.

$sin\theta = \frac{oppositeside}{hypotenuse} , sin 45 = 0.707, 0.707 = \frac{0.5x}{24.498}.$

$x= \frac{(0.707)(24.498)}{0.5} = 34.640$

So x measures 34.640 units.