Question

HELP!!!!

In a right triangle with a leg of 4 and a hypotenuse of 8, find the measures of all angles.

Answer 1

Answer: 90° , 60° and 30° .

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=(4)/(8)=(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)=(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° .