This is trigonometry! I need help with what it means when it says “adjacent for 20 degrees” , “hypotenuse for 20 degrees” etc. ! Thanks

Adjacent for 20° = 17.3mm

Hypotenuse for 70° = 120mm?

Opposite for 70° = 17.3mm

Hypotenuse for 20° = 120mm?

Adjacent for 70° = 10mm

Opposite for 20° = 10mm

Step-by-step explanation:

I think "Adjacent for 20°" is asking the length of the side adjacent to 20° (Although the Hypotenuse is adjacent to 20° don't answer its length because Hypotenuse are ALWAYS opposite to the 90° of a right triangle). The "Opposite for 70°" is asking the length of side opposite to 70°.

Also, I really don't know why the hypotenuse is 120mm because by the Pythagorean Theorem, it should 19.98mm (20mm if rounded to the nearest tenths).

  "adjacent" is the short ray that makes up the angle. "opposite" is the side not touching the angle.

Step-by-step explanation:

Since your question text involves identifying adjacent and opposite, that's what we'll explain.

In a right triangle, the hypotenuse is the side opposite the right angle. For the purposes here, it is always referred to as the hypotenuse. It is the longest side in the right triangle.

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Each acute angle in the right triangle has the hypotenuse on one side. The other side forming the angle is called the adjacent side.

The remaining side of the triangle (not the hypotenuse, and not the adjacent side) is the one opposite the angle. It is called the opposite side.

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In the first attachment is a triangle with sides and angles labeled. Each angle is labeled with an upper-case letter (A, B, C), and each side opposite that angle is labeled with the corresponding lower-case letter (a, b, c). This is a customary way to label triangle sides and angles. (The right angle is not always C.)

So, for angle A, the hypotenuse is c, and the adjacent side is b. The side opposite is a.

For angle B, the hypotenuse is c (still), and the adjacent side is a. The side opposite is b.

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The second attachment applies these ideas to your first (upper left) triangle.

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As for the applicable formulas, the mnemonic SOH CAH TOA is often helpful. It is intended to remind you that ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Then the applicable formulas clockwise from left are for Cos, Sin, Cos.

"What went wrong" in the 30° triangle is that somebody used a calculator in radians mode, not degrees mode, when they tried to compute the sine. A couple of errors were made, because sin(30 radians) is about -0.988, so the minus sign was dropped, too. (You always need to check that the calculator is in the right mode.)