Respuesta :
Answer:
The remaining sides are [tex]\frac{8}{\sqrt{3}}[/tex] units and [tex]\frac{4}{\sqrt{3}}[/tex] units.
Step-by-step explanation:
It is given that the interior angles of a right angle triangle are 30, 60, 90 degree. The side opposite of 60 degrees is 4.
In a right angle triangle,
[tex]\sin \theta = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sin (60) = \dfrac{4}{hypotenuse}[/tex]
[tex]\dfrac{\sqrt{3}}{2} = \dfrac{4}{hypotenuse}[/tex]
[tex]hypotenuse =4\times \dfrac{2}{\sqrt{3}}[/tex]
[tex]hypotenuse =\dfrac{8}{\sqrt{3}}[/tex]
The hypotenuse of the triangle is [tex]\dfrac{8}{\sqrt{3}}[/tex] units.
According to the Pythagoras theorem,
[tex]hypotenuse^2 =perpendicular^2+base^2[/tex]
[tex](\dfrac{8}{\sqrt{3}})^2 =(4)^2+base^2[/tex]
[tex]\dfrac{64}{3} =16+base^2[/tex]
[tex]\dfrac{64}{3}-16=base^2[/tex]
Taking square root on both sides.
[tex]\sqrt{\dfrac{64-48}{3}}=base[/tex]
[tex]\sqrt{\dfrac{16}{3}}=base[/tex]
[tex]\dfrac{4}{\sqrt{3}} =base[/tex]
Therefore, the remaining sides are [tex]\frac{8}{\sqrt{3}}[/tex] units and [tex]\frac{4}{\sqrt{3}}[/tex] units.
