Question

Help please. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

A.5√2 /2

B.5√3

C.5√2

D.5√3 /2

Answer 1

Answer: The value of the variable is
`x=(5\sqrt2)/(2).`

Step-by-step explanation: We are given to find the value of the variable 'x' in the figure.

We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:

h = 5 units.

Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.

That is, p = x units.

From relations between trigonometric ratios, we have

`\sin 45^\circ=\frac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow (1)/(\sqrt2)=(p)/(h)\\\\\\\Rightarrow (1)/(\sqrt2)=(x)/(5)\\\\\\\Rightarrow x=(5)/(\sqrt2)\\\\\\\Rightarrow x=(5\sqrt2)/((\sqrt2)^2)\\\\\\\Rightarrow x=(5\sqrt2)/(2).`

Thus, the value of the variable is
`x=(5\sqrt2)/(2).`