Question

a right triangle with an angle of approximately 53.1 is inscribed in the first quadrant of the unit circle with a horizontal length of 3/5 and a vertical length of 4/5 complete the table for the following trigonometric functions

Answer 1

Answer: Angles: 53.1°, 90°, 39.9°

horizontal lenght: 3/5

vertical lenght: 4/5

hypotenuse: 1

Step-by-step explanation:

We have that:

Angle = 53.1°

Horizontal lenght = 3/5 (this is the adjacent cathetus)

Vertical lenght = 4/5 (this is the opposite cathetus)

We can check this using that

tg(angle) = opposite/adjacent:

tg(53.1) = 1.33

and

(4/5)/(3/5) = 4/3 = 1.33

so this makes sense.

Now, we can find the hypotenuse by the relation:

Sin(angle) = opposite/hypotenuse:

sin(53.1) = (4/5)/H

H = (4/5)/sin(53.1) = 1

Now, in a triangle rectangle we always have an angle of 90°.

And we know that the addition of the 3 internal angles of a triangle rectangle always add up to 180°, so we can find the last angle with this.

A + 53.1° + 90° = 180°

A = 90° - 53.1° = 36.9°

Now we have finded all the missing parts of our triangle.