Answer:
Answer: x is 5 units
Step-by-step explanation:
» From trigonometric ratios,
[tex]{ \tt{ \red{ \sin( \theta) = \frac{opposite}{hypotenuse} }}} \\ [/tex]
- theta is 45°
- opposite is x
- hypotenuse is √50
[tex]{ \tt{ \sin(45 \degree) = \frac{x}{ \sqrt{50} } }} \\ \\ { \tt{x = \sqrt{50} \times \frac{1}{ \sqrt{2} } }} \\ \\ { \tt{x = \sqrt{ \frac{50}{2} } }} \\ \\ { \tt{x = \sqrt{25} }} \\ { \boxed{ \tt{x = 5 \: units}}}[/tex]
Or, from pythogras theorem
[tex]{ \tt{ {a}^{2} + {b}^{2} = {c}^{2} }}[/tex]
- a is x, and b is x
- c is √50
[tex]{ \tt{ {x}^{2} + {x}^{2} = {( \sqrt{50}) }^{2} }} \\ { \tt{2 {x}^{2} = 50 }} \\ { \tt{ {x}^{2} = 25}} \\ { \tt{x = \sqrt{25} }} \\ { \boxed{ \tt{x = 5 \: units}}}[/tex]
