Physics, 16.03.2020 20:32 kayleewoodard

A guy wire to a tower makes a 67 degree angle with level ground. At a point 33 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the pole is 38 degrees. Find the length if the wire ( nearest foot).

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Answer from: kmsg2000

The length of wire is 67.3 ft.

Given data:

The angle between the tower and level ground is, $\theta = 67^{\circ}$ .

The distance from the tower is, d = 33 ft.

The angle of elevation is, $\theta'=38^{\circ}$ .

Let us consider the height of tower as H and length of sire be L. Then as the concept of trigonometry, the relation between the Height( vertical parameter) and Length ( horizontal parameter) is given as,

$sin\theta = \dfrac{H}{L}\\\\H = sin \theta \times L\\\\H = sin67 \times L$

Now, at 33 ft distance, the angle of elevation becomes 33 Degrees. So, the expression is,

$sin \theta' = \dfrac{H}{L+d}\\\\sin38 = \dfrac{(sin67 \times L)}{L+33}\\\\sin38(L+33)=sin67 \times L\\\\L = 67.3\;\rm ft$

Thus, we can conclude that the length of wire is 67.3 ft.

Learn more about the Trigonometric ratios here:

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Answer from: kingethan08

Length of the wire = 67.3 feet

Explanation:

H = height of the tower

L = length of the guy wire

sin(67 ) = H / L

H = L*sin(67)

Add 33 ft to L, and the angle is now 38 deg. So

sin(38) = H / (L + 33)

Using the 1st equation, substitute for H:

sin(38) = L* sin(67) / (L + 33)

Plug in numbers and rearrange

0.615 = L*0.920 / (L + 33)

0.615*L + 20.2 = 0.920*L

0.30*L = 20.2

L = 67.3 feet

CHECK:

H = 67.3*sin(67) = 61.94 ~ 62

H = (67.3 + 33)*sin(38) = 61.75 ~ 62

Answer from: Quest

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006 kilo calorie

then ,802.3 kilo joule will be = 802.3 $\times$ 0.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

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