Answer:
The answer to your question is log₁₀ x + b = a
Step-by-step explanation:
General formula
Logarithmic function Exponential function
log ₐ b = c
a = antilogaritm c = exponent
b = base b = base
c = logaritm a = power
In your problem
10 = base
a = exponent
x + b = power
Exponential function log₁₀ x + b = a
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Explanation:
A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram
The diagram below shows all of this visually summarized. We have the segments
And we have these angles
Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.
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Once the diagram is set up, we'll use the law of cosines to find x.
Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.
The interior angles of triangle ABC are
The sides opposite the angles are
Now we can apply the law of cosines
b^2 = a^2 + c^2 - 2*a*c*cos(B)
x^2 = 483^2 + 550^2 - 2*483*550*cos(79)
x^2 = 434412.180756441
x = sqrt(434412.180756441)
x = 659.099522649229
x = 659
Side AC, or CA, is roughly 659 miles long.
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To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)
Distance Traveled = AB + BC + CA
Distance Traveled = 550 + 483 + 659
Distance Traveled = 1692 miles
