Two wires support an electricity pole. if the wires make angles of 58°and 67° with the ground and |AB|=21m, calculate the lengths of the wires
sorry steve you failed
All angles of a triangle add up to 180
degrees, so you have 2 angles you can
Find the third angle by 180-58-67=55
Now use the law of sines...(capital
is the angle and lower case the
side across from said angle
you have the 3 angles now and 1 side
use law of sines
a/sinA=b/sinB=c/sinC
(law of cos is for if you know sides
but not angles)
(law of tan if you know 3 of the 4
unknowns c^2=a^2+b^2-2abcos(C) )
well the top angle(C) is 55
which means AB would be across from
it being 21
so
a/sin58=b/sin67=21/sin55
so because c=21/sin55=
a=21/sin(55 deg)*sin(58 deg)
b=21/sin(55 deg)*sin(67 deg)
so
a = 21.7407868825
b = 23.5983076125
now just test this using tan
(remember bedmas order of operations)
2*21.7407868825*23.5983076125*cos(55 deg)
=588.541936444
=2*
21.7407868825^2+23.5983076125^2
=1029.541936444
1029.541936444-588.541936444
=441
and 21^2 =.....drumroll please
441 on the nose!
and i have been out of school for 20 years
To find the lengths of the wires, we can use trigonometry. We will use the tangent function to determine the lengths of the wires.
Let's denote the lengths of the wires as x and y.
First, let's find x.
From the given information, we know that the angle between the ground and one wire is 58°. We can set up the following equation using the tangent function:
tan(58°) = x / 21m
To find x, we rearrange the equation:
x = 21m * tan(58°)
Using a calculator, we find:
x ≈ 28.47m
Now, let's find y.
Similarly, using the other angle of 67°:
tan(67°) = y / 21m
To find y, we rearrange the equation:
y = 21m * tan(67°)
Using a calculator, we find:
y ≈ 33.73m
Therefore, the lengths of the wires are approximately 28.47m and 33.73m.
To find the lengths of the wires, we can use trigonometry. Let's break down the problem step by step.
1. Draw a diagram: Draw a diagram to visualize the problem. Label the points A and B, representing the points where the wires are attached to the ground. Also, label the angles A and B, representing the angles the wires make with the ground.
|\
| \ Pole
| \
|_ _ __\____ Ground
2. Identify the given information: From the problem, we are given the angles A = 58° and B = 67°. Additionally, we are given the distance between the attachment points of the wires, |AB| = 21m.
3. Solve for the lengths of the wires: Let's calculate the lengths of the wires individually.
- Wire A: To find the length of Wire A, we need to use the trigonometric function cosine (cos) since we have the adjacent side and the angle A. Recall that in a right triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse. Using this formula, we can write:
cos(A) = Adjacent side / Hypotenuse
cos(58°) = |AB| / Length of Wire A
Solving for the length of Wire A:
Length of Wire A = |AB| / cos(58°)
- Wire B: Similarly, to find the length of Wire B, we will use the same trigonometric function, cosine (cos), since we have the adjacent side and the angle B. Applying the formula:
cos(B) = Adjacent side / Hypotenuse
cos(67°) = |AB| / Length of Wire B
Solving for the length of Wire B:
Length of Wire B = |AB| / cos(67°)
4. Calculate the lengths: Now, substitute the values we have and calculate the lengths of the wires:
Length of Wire A = 21m / cos(58°)
Length of Wire B = 21m / cos(67°)
Using a calculator, we can find the values of these lengths:
Length of Wire A ≈ 30.66m (rounded to two decimal places)
Length of Wire B ≈ 23.62m (rounded to two decimal places)
Therefore, the length of Wire A is approximately 30.66 meters, and the length of Wire B is approximately 23.62 meters.
Draw a diagram. If the pole has height h, then
h = 21/(cot58°-cot67°) = 104.8
The two wires have length
104.8 csc67° = 113.9
104.8 csc58° = 123.6