Question

Find the value of x. *

50 PTS!

5
25
5√2
50

Answer 1

Answer: x is 5 units

Explanation:

» From trigonometric ratios,

`{ \tt{ \red{ \sin( \theta) = (opposite)/(hypotenuse) }}} \\`

• theta is 45°
• opposite is x
• hypotenuse is √50

`{ \tt{ \sin(45 \degree) = (x)/( √(50) ) }} \\ \\ { \tt{x = √(50) * (1)/( √(2) ) }} \\ \\ { \tt{x = \sqrt{ (50)/(2) } }} \\ \\ { \tt{x = √(25) }} \\ { \boxed{ \tt{x = 5 \: units}}}`

Or, from pythogras theorem

`{ \tt{ {a}^(2) + {b}^(2) = {c}^(2) }}`

• a is x, and b is x
• c is √50

`{ \tt{ {x}^(2) + {x}^(2) = {( √(50)) }^(2) }} \\ { \tt{2 {x}^(2) = 50 }} \\ { \tt{ {x}^(2) = 25}} \\ { \tt{x = √(25) }} \\ { \boxed{ \tt{x = 5 \: units}}}`

Answer 2

• Option A

Explanation:

We can solve this with the help of Pythagoras theorem.

• => (√50)² = x² + x²
• => √50 x √50 = x² + x²
• => 50 = 2x²
• => 25 = x²
• => x = 5

Hence, the value of x is 5 units.