a 12-ft-long guy wire is attached to a telephone pole 10.5 ft from the too of the pole. If the water forms a 52 degree angle with the ground, how high is the telephone pole?
water ?
let the distance from the point of attachment to the ground be h
sin52° = h/12
h = 12sin52
= ...
add 10.5 to h to get the height of the pole
20 feet
To find the height of the telephone pole, we can use trigonometry.
Let's define the variables:
h = height of the telephone pole (what we need to find)
d = distance from the bottom of the pole to the point where the guy wire is attached (10.5 ft)
L = length of the guy wire (12 ft)
θ = angle formed between the guy wire and the ground (52 degrees)
We can use the sine function to solve for the height:
sin(θ) = h / L
Rearranging the equation, we get:
h = L * sin(θ)
Substituting the known values, we have:
h = 12 ft * sin(52 degrees)
To calculate the value, we need to convert 52 degrees to radians because most trigonometric functions work with radians. To convert degrees to radians, use the formula:
radians = degrees * (π / 180)
So, in radians, 52 degrees is:
52 * (π / 180) radians
Substituting this value into the equation, we have:
h = 12 ft * sin(52 * (π / 180))
Now, let's calculate this using a calculator or mathematical software:
h ≈ 9.16 ft
Therefore, the height of the telephone pole is approximately 9.16 ft.