Answer:
The boat is approximately 338.74 feet from the base of the cliff. If the problem suggests rounding to the nearest whole number, you should use 339 ft.
Step-by-step explanation:
Let's draw the right angle triangle associated with the problem (see attached image). Notice that the 305 ft height corresponds to the "opposite side" to the given acute angle of
, and that the distance we need to find is the "adjacent" side to the given acute angle. Therefore, the appropriate trigonometric function to use is the "tangent", given that from it we can solve for the unknown adjacent side "x":
![tan(42^o)=\frac{opposite}{adjacent} \\tan(42^o)=\frac{305}{x}\\x=\frac{305}{tan(42^o)}\\ x=338.74\,\, ft](https://tex.z-dn.net/?f=tan%2842%5Eo%29%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D%20%5C%5Ctan%2842%5Eo%29%3D%5Cfrac%7B305%7D%7Bx%7D%5C%5Cx%3D%5Cfrac%7B305%7D%7Btan%2842%5Eo%29%7D%5C%5C%20x%3D338.74%5C%2C%5C%2C%20ft)
Since the first car travels 55 miles per hour and starts an hour early, by 4:00 it is 55 miles away from the other car. Therefore, the equation is 55+a(some value)+b(another value)=380. If a car travels 55 miles per hour, that means that we add 55 for each hour and 55*x (if x is the number of hours) is the distance traveled. We have accounted for the first hour, so this is similar to saying that they start 55 miles away at 4:00 and go from there. For the other car, since it travels 75 miles per hour, its distance in hours is 75*x (the amount of time spent should be the same if we start at 4:00). Therefore, since they travel away from each other, our total distance is 55+55x+75x=380. Subtracting 55 from both sides (and combining like terms), we get 130x=325. Next, we divide both sides by 130 to get 2.5 hours, or 2 hours and 30 minutes
Answer: The measure of ∠ABC = 54°.
Step-by-step explanation:
As we know that
Measure of major arc AC = 234° ( Far arc)
Measure of minor arc AC = 126° (Near arc)
By theorem, we know that the angle formed by intersection of two tangents is equal to half the difference of far arc and near arc.
As we know that ∠ABC is given by
![\frac{1}{2}(Far\ arc-Near\ arc)\\\\=\frac{1}{2}(234-126)\\\\=\frac{1}{2}\times 108^\circ\\\\=54^\circ](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28Far%5C%20arc-Near%5C%20arc%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%28234-126%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20108%5E%5Ccirc%5C%5C%5C%5C%3D54%5E%5Ccirc)
Hence, the measure of ∠ABC = 54°.
Answer:
x = 0/2
x = 0
Step-by-step explanation:
4(x+8)-2(x-7) = 46
Expanding the brackets
4x +32 - 2x +14 = 46
2x + 46 = 46
2x = 46-46
2x = 0
x = 0/2
x = 0
3/4 is the same as 6/8 not sure what that model is called though