Question

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

Answer 1

45 45 90 triangle
Ratio of leg : hypo = x : x√2

Given hypo x = 5
So leg = 5/ √2 = 5√2 / 2

Answer
A. 5√2 / 2

Answer 2

Answer: a.
`(5√(2))/(2)`

Explanation:

In the given picture we have aright triangle with Length of Hypotenuse = 5 units.

By using trigonometric ratios , we have

`\sin\theta=\frac{\text{side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\sin45^(\circ)=(x)/(5)\ \ [\because \sin 45^(\circ)=(1)/(√(2))]\\\\\Rightarrow\ (1)/(√(2))=(x)/(5)\\\\\Rightarrow\ x=(5)/(√(2))`

Rationalize :
`x=(5)/(√(2))*(√(2))/(√(2))=(5√(2))/(2)`

Hence, the value of x =
`(5√(2))/(2)`