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2 years ago

Help with this Math problem pleas?

Mathematics

1 answer:

victus00 [196]2 years ago

8 0

This a pretty typical right triangle trig problem; the first step is to figure out what we have and what we want in relation to an acute angle in the problem.

Here we have a right triangle, G=90°, and we're given angle F=23°. So we have to name everything in relation to F.

31 = FG is <em>adjacent </em>to F.

x = GE is <em>opposite </em>to F.

OK, we have an opposite and adjacent; that tells us we need to use the tangent of F. Let's write it:

tan 23° = tan F = opp/adj = x/31

Solving,

x = 31 tan 23°

I hate the calculator part. I used to love that part.

x = 31 tan 23° ≈ 13.16 feet

Answer: 4) x ≈ 13.2 ft

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an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
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We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
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Second equation
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n/2 (a₁ + an) = 437
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n(x - 4) = 874
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Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.

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