Answer:
d = 8.24
Step-by-step explanation:
You want the measure of d, the side opposite the 31° angle in the right triangle shown as having a hypotenuse of length 16.
Trig ratios
The mnemonic SOH CAH TOA was invented to remind you of the relations between sides and trig functions in a right triangle. In the triangle shown, you have an angle, the side opposite (O), and the hypotenuse (H). The relevant trig relation is ...
Sin = Opposite/Hypotenuse
Application
Filling in the values shown, this tells you ...
sin(31°) = d/16
Multiplying by 16 gives the value of d:
d = 16·sin(31°)
Your calculator can tell you what this value is, rounding it if you want.
The value of d is 8.24.
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Additional comment
The other parts of the mnemonic tell you ...
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
You will notice the flag in the lower left corner of the calculator display tells you the mode is set to Degrees (DEG), rather than radians (RAD) or grads (GRA). This is required in order for sin(31) to be properly interpreted.
