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vitfil [10]
2 years ago
11

A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After pl

acing the pole, Zachary measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

Mathematics
1 answer:
sammy [17]2 years ago
4 0

The length of the guy's wire to the nearest foot is 89 feet.

The situation forms a right-angled triangle.

<h3>Properties of a right angle triangle:</h3>
  • A right-angle triangle has one angle of 90 degrees.
  • The sides can be found using the Pythagoras theorem.
  • The angles can be found using trigonometric ratios.

The hypotenuse of the triangle is the length of the wire.

let's use the smaller triangle to find the angle opposite the tower. Therefore,

tan ∅ = opposite / adjacent

tan ∅ =  5 / 2

∅ = tan⁻¹ 2.5

∅ = 68.1985905136

∅ = 68.20°

Therefore,

cos 68.20 = adjacent / hypotenuse

cos 68.20 = 33 / hypotenuse

hypotenuse = 33 / cos 68.20

hypotenuse = 88.8606843161

Therefore,

length of wire ≈ 89 feet.

learn more on triangles here; brainly.com/question/25762788?referrer=searchResults

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5a + 18 &lt; −27 pre algibra
Grace [21]

Answer:

X < -9

Step-by-step explanation:

5a +18 < -27

5a < -27 -18

5a < - 45

5a/5 < - 45/5

a < - 9

Answred by Gauthmath

5 0
3 years ago
Read 2 more answers
A cosine function has a period of 5, a maximum value of 20, and a minimum value of 0. The function is not a reflection of its pa
Alika [10]

Answer:

  A:  f(x)=10cos(2π/5 x)+10

Step-by-step explanation:

The coefficient of x in the cosine argument of the function will be 2π/period. Since the period is 5, the coefficient is 2π/5. This observation eliminates choices B and C.

The description "not a reflection of the parent function over the x-axis" means the multiplier of the cosine function is not negative, eliminating choice D.

The remaining choice A matches the description.

7 0
3 years ago
2(5-3v)+9v=28 step by step please
Irina-Kira [14]
First, distribute the 2 across the parenthesis.
10-3v+9v=28
Combine like terms on the left.
10+6v=28
Start to get the numbers on the right and the v alone on the left by moving the 10 to the right.
6v=28-10
6v=18
Divide to get the v alone.
v=3

Hope that helps.
4 0
3 years ago
A rock is thrown upwards from the edge of a 52 foot cliff and eventually falls to the ground. The graph
Lina20 [59]
The rock's height is increasing in the interval from 0 seconds to 3 seconds.

At time 0 the rock starts moving upward from 52 foot until it reachs 180 foot height (time 3 seconds). Then the rock starts to descend, which means that the height starts to decrease.
5 0
3 years ago
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I need the answer to a parts I-iii and the answer to b
fomenos

Answer:

a)

i) Mean = 72

ii) Median = 72

iii) Mode = 72

b)

69, 70, 71, 72, 72, 72, 73, 74, 75

Step-by-step explanation:

<u>a. To find mean, median and mode</u>

It is given that all the 9 students get 72 marks.

Therefore the data set be,

72, 72, 72, 72, 72, 72, 72, 72 72

<u>i) mean </u>= (sum of data)/(total number of data)

 = (9 * 72)/9 = 9

<u>ii) Median </u>- Central data in the data set when arranging ascending or descending order

72, 72, 72, 72, 72, 72, 72, 72 72

Median = 72

<u>iii) Mode </u>- Most repeating data in the data set

Here mode = 72

<u>b). To find a data set</u>

69, 70, 71, 72, 72, 72, 73, 74, 75

Here Mean, mode and median are all 72

3 0
3 years ago
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