Please assist with the geometry questions part 1

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  1.  sin(x) = a/c; cos(x) = b/c; tan(x) = a/b

  2, 3 see below

Step-by-step explanation:

1. The mnemonic SOH CAH TOA reminds you of the relationships between trig functions and sides of a right triangle:

  Sin = Opposite/Hypotenuse   ⇒   sin(x) = a/c

  Cos = Adjacent/Hypotenuse   ⇒   cos(x) = b/c

  Tan = Opposite/Adjacent   ⇒   tan(x) = a/b

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2. The attachment shows the two special right triangles. The 30-60-90 right triangle has sides in the ratio 1 : √3 : 2. The 45-45-90 isosceles right triangle has sides in the ratio 1 : 1 : √2.

These ratios can be used to write proportions that help you find the length of a missing side.

Example:

Suppose the triangle in problem 1 has x = 30°, and a = 10. Then we could find the length of missing side 'c' using a proportion involving the short side and the long side (hypotenuse).

  2/1 = c/10   ⇒   c = 20

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3. In a right triangle, the acute angles are complementary. The side adjacent to one acute angle is the side opposite the other. So the sine of one of the angles is the cosine of the other, and vice versa. This means the sine of an angle is the cosine of its complement, and vice versa.

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Comment on question 3

The wording of this question is a little strange. Sine and cosine are not complementary. Rather, the angles for which those functions have the same value are complementary.