Answer:
11. 39.0°
12. 31.0°
Explanation:
The mnemonic SOH CAH TOA reminds you of the relations between trig functions and the angles and sides in a right triangle.
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11.
The hypotenuse and the side opposite the unknown angle are given. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(x°) = 39/62
The angle is found using the inverse sine function.
x° = arcsin(39/62) ≈ 39.0°
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12.
The hypotenuse and the side adjacent to the unknown angle are given. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(x°) = 84/98
The angle is found using the inverse cosine function.
x° = arccos(84/98) ≈ 31.0°
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Additional comments
These functions are found using a calculator. As shown in the attachment, the calculator must be set to show angles in degrees (not radians or grads). (This mode setting is shown in the lower left corner of the display: DEG.)
As shown in the attachment, these inverse functions are often the "second" function of the trig function keys of the calculator.
You can read these inverse functions as ...
arcsin(Q) = sin⁻¹(Q) ≡ "the angle whose sine is Q"
arccos(Q) = cos⁻¹(Q) ≡ "the angle whose cosine is Q"