Question

How do you find A to the nearest degree?

Answer 1

m∠A ≈ 67°

Explanation:

It's a right triangle, because:

`5^2+12^2=13^2\\25+144=169\\169=169`

Pythagorean teorem.

Use sine:

`sine=(opposite)/(hypotenuse)`

We have:

`opposite=12\\hypotenuse=13`

`\sin A=(12)/(13)\approx0.9231\Rightarrow67^o`

Answer 2

A ≈ 67°

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°

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Cos(A) = Adjacent/Hypotenuse = 5/13

A = arccos(5/13) ≈ 67°

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

A = arctan(2.4) ≈ 67°

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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)