Question

HELP!!!!

Answer 1

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 $\theta$  in the triangle.

Then by trigonometry , we have

$\sin\theta=\dfrac{4}{8}=\dfrac{1}{2}$  [Sine of an angle is the ration of the side opposite to the angle and the hypotenuse of a right triangle.]

Also , $\sin 30^{\circ}=\dfrac{1}{2}$

$\Rightarrow\ \theta = 30^{\circ}$

Let  x be the measure of the third angle.

BY Angle sum property of triangle , we have

$90^{\circ}+30^{\circ}+x= 180^{\circ}\\\\ 120^{\circ}+x= 180^{\circ}\\\\ x=180^{\circ}-120^{\circ}\\\\ x= 60^{\circ}$

Therefore , the measures of all angles in the triangle : 90° , 60° and 30° .