Answer:
- 48°
- 42°
Explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides in a right triangle:
- Sin = Opposite/Hypotenus
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
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application
In these triangles, you are given all three sides, so you can determine the angle from any pair of them you might like. If you choose the opposite and adjacent sides, you have ...
1.
tan(?) = 72/65
? = arctan(72/65) ≈ 48°
2.
tan(?) = 65/72
? = arctan(64/72) ≈ 42°
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Additional comment
You will recognize that these triangles have the same side measures. The two angles are the two acute angles in the triangle, so one is the complement of the other: 42° = 90° -48°.
The calculator is shown in the attachment for two reasons. (1) The mode needs to be set to degrees (lower left of display). (2) The inverse tangent function is usually the "2ND" function of the "Tan" key. That is, you must press the 2ND key, then the Tan key in order to get the arctangent.
Of course, you can use any of a number of apps or web sites to solve these triangles for you. An example is shown in the second attachment.
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SOH CAH TOA applies to right triangles. You can solve any right triangle given at least one side and one acute angle (or two sides). Determine how the side(s) relate(s) to the angle (adjacent, opposite, hypotenuse) and fill in the values in the relevant trig relation. Solve that relation for the missing value. Of course, the angle sum theorem and the Pythagorean theorem apply, so you may not need trig relations for what you have to find.