Answer: 90° , 60° and 30° .
Step-by-step explanation:
Given : In a right triangle with a leg of 4 units and a hypotenuse of 8 units.
One angle should be 90°. (A right triangle has a 90° angle.)
Let the given leg is the side opposite to the angle [tex]\theta[/tex] in the triangle.
Then by trigonometry , we have
[tex]\sin\theta=\dfrac{4}{8}=\dfrac{1}{2}[/tex] [Sine of an angle is the ration of the side opposite to the angle and the hypotenuse of a right triangle.]
Also , [tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]
[tex]\Rightarrow\ \theta = 30^{\circ}[/tex]
Let x be the measure of the third angle.
BY Angle sum property of triangle , we have
[tex]90^{\circ}+30^{\circ}+x= 180^{\circ}\\\\ 120^{\circ}+x= 180^{\circ}\\\\ x=180^{\circ}-120^{\circ}\\\\ x= 60^{\circ}[/tex]
Therefore , the measures of all angles in the triangle : 90° , 60° and 30° .
