Two different buses start their routes at the same corner at 9 A.M. Buses from one route stop at the library every 9 minutes. Bu
1 answer:
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Answer:
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.
<em>Example</em>:
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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<em>Comment on question 3</em>
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.
Answer:
1. No
2. 1,050 bushels of corn
Step-by-step explanation:
1. A number is proportional if it has a constant ratio to another quantity.
8/12 and 10/25 do not.
2. An acre will produce bushels of corn.
750 divided by 10 is 75. <u>This is 75 bushels per acre.</u>
Then you would multiply 75 and 14.
This equals 1,050 bushels of corn.