Answer: x = 19.7 (choice C)
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Explanation:
The reference angle is 24 degrees. Opposite that angle is the side 8 units long. The horizontal portion is unknown and it's the adjacent side.
Also unknown is the value of x which is the hypotenuse.
To summarize:
- opposite = vertical leg = 8
- adjacent = horizontal leg = unknown
- hypotenuse = x
The hypotenuse is always opposite the 90 degree angle.
To tie together the opposite and hypotenuse, we'll use the sine ratio
sin(angle) = opposite/hypotenuse
sin(24) = 8/x
x*sin(24) = 8
x = 8/sin(24)
x = 19.6687 approximately
x = 19.7 after rounding to the nearest tenth.
Side note: your calculator needs to be in degree mode
