How do you find a to the nearest degree?

  A ≈ 67°

Step-by-step explanation:

Since you have all three sides of the right triangle, you can use any of the inverse trig functions to find the angle. SOH CAH TOA reminds you ...

  Sin(A) = Opposite/Hypotenuse = 12/13

  A = arcsin(12/13) ≈ 67°

__

  Cos(A) = Adjacent/Hypotenuse = 5/13

  A = arccos(5/13) ≈ 67°

__

  Tan(A) = Opposite/Adjacent = 12/5 = 2.4

  A = arctan(2.4) ≈ 67°

_____

Comment on calculator use

When you use your calculator for these inverse functions, make sure it is in "degrees" mode (not "radians"). Your calculator keys may be labeled with a "-1" superscript to indicate the inverse function. You can use the rounding function of your calculator, or you can round the number yourself (probably easier).

  sin⁻¹ = arcsin

  cos⁻¹ = arccos

  tan⁻¹ = arctan

A Google search box is also capable of showing you the inverse trig function value. (see attachment)

Step-by-step explanation:

It's a right triangle, because:

Pythagorean teorem.

Use sine:

We have:

i'm assuming that it's c.)   volcanoes built the mountains and earthquakes tore them down.