Are the angles 117 in degrees and 477 in degrees coterminal?

Yes, they are coterminal.

Step-by-step explanation:

Coterminal angles are angles that are in multiples of -360 degrees or +360 degrees away from the initial angle.

Therefore, the easiest way to check if an angle is coterminal is set up an equation.

We get a true statement, which means that 117 is a coterminal angle of 477 and 477 is a coterminal angle of 117.

We can also determine the value in radians.

117° in radians is . Coterminal angles for radians are multiples of , either negative or positive.

However, we also need to determine the value of 477 in radians too.

So, if we add to :

Therefore, even in radians, 477° is an angle coterminal to 117°.

You are given 117°.

To find angles that are coterminal with 117°, we do the following:

117° + 360° = 477°

117° - 360° = 243°

As you can see, when we added 117° to 360°, we got 477°.

To answer your question, YES.

You now know that 117° and 477° are coterminal angles.

Keep in mind that 477° is not the only coterminal angle to 117°.

You can calculate the area of the triangle knowing its sides.
 For this, we use Heron's formula:
 Area = root ((s) * (s-a) * (s-b) * (s-c))
 s = (a + b + c) / 2
 Where,
 a, b, c: sides of the triangle
 s: semi-perimeter
 The sides of the triangle are:
 For AB:
 AB = root ((- 1 - (- 7)) ^ 2 + (5 - (- 1)) ^ 2)
 AB = 8.485281374
 For AC:
 AC = root ((0 - (- 7)) ^ 2 + (0 - (- 1)) ^ 2)
 AC = 7.071067812
 For BC:
 BC = root ((0 - (- 1)) ^ 2 + (0-5) ^ 2)
 BC = 5.099019514
 Using the formulas we have:
 s = (8.485281374 + 7.071067812 + 5.099019514) / 2
 s = 10.32768435
 Area = root ((s) * (s-a) * (s-b) * (s-c))
 Area = root ((10.32768435) * (10.32768435-8.485281374) * (10.32768435-7.071067812) * (10.32768435-5.099019514))
 Area = 18
 
 the area of triangle ABC is:
 Area = 18