Identify the correct trigonometry formula to use to solve for x.
2 answers:
Answer: Third option.
Step-by-step explanation:
Given the right triangle in the figure attached, you know that, for the known angle of 62 degrees, the lenght of the opposite side is 18 and the hypotenuse is "x"
Therefore, you need to remember the following identity:
Then, having that:
You need to substitute these values into , then you get that the correct trigonometry formula to use to solve for "x" is:
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To turn into a fraction you should do such steps:
1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 0.(6), so you have x=0.666... .
2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 6. Now multiply both sides of the equation by
. Thus, you have
or
.
3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, .
4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: . If you divide both sides by 9, you get
. When simplified, you get that
.
Answer: .