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Answer:tan (60) = √3
Explanation:The triangle in question is a right triangle; hence, we will apply the Pythagorean theorem to find the length of the unknown side.
unknown side = sqrt [(hypotenuse)^2 + (other side)^2]
unknown side = 21√3 units
Given it is a right triangle, we can utilize special trigonometric ratios.
Thus:
tan θ = opposite / adjacent
In this triangle:
θ = 60°
Opposite side = 21√3
Adjacent side = 21
Now substituting into the equation to calculate tan 60 gives us:
tan (60) = (21√3) / (21) = √3
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First find the amount of tax: 98.90 - 92 = 6.9. Next, compute the tax rate by dividing the tax by the pre-tax price: 6.9 / 92 =.075. Convert to a percentage by multiplying by 100:.075 * 100 = 7.5. Thus the tax rate is 7.5%.
The distance can be defined by the equation

The relationship of distance over time is expressed as


When t=2s,


An error of 12.8 feet arises.
b) Now considering t=5 seconds



An error of 32 feet occurs.
To provide clarity, consider this explanation: There are five runners on the team, and they finished consecutively. The total points earned are 55. Let's denote the position of the first runner as p. Therefore: 1st = p, 2nd = p + 1, 3rd = p + 2, 4th = p + 3, and 5th = p + 4. The sum of their placements equates to 55: (1st + 2nd + 3rd + 4th + 5th) = 55, simplifying to (p + p + 1 + p + 2 + p + 3 + p + 4) = 55, results in the equation: 5p + 10 = 55. Therefore, 5p = 45, leading to p = 9. Thus, their placements are: 1st = 9th, 2nd = 10th, 3rd = 11th, 4th = 12th, and 5th = 13th.