A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67 degree and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole?
Here, I assume that the 67 degree angle is between the guy-wire and the pole, otherwise the height of the attachment point at the top of the pole will be ridiculously high: 137 ft x tan67 = 137 x 2.356 =322.7 ft (unrealistic), some giant transmission towers may reach such height, but the do not employ guy-wires, they are selp-supporting steel structures with a wide base.
so instead, I use cotangent of 67 deg or tan(90 -67)deg = tan 23 deg = ctg 67 deg = 0.425
The distance from ground of the point of attachment of guy-wire and the pole is 137 ft x 0.425 = 58.225 ft
Usually the angle between the guy-wire and the pole is 25 deg. to 45 deg. 30 degrees is very common. In some situations, because of a structure such as a street or a bridge, the angle between the pole and the guy-wire may have to be stretched, flattened (increased).
To find the height of the pole, we can use trigonometry.
Let's label the height of the pole as "h". We also have the length of the guy-wire and the distance from the base of the pole to the point where the wire is attached to the ground.
Here's how we can solve it step-by-step:
1. Draw a diagram: Sketch a right triangle where the pole represents the vertical side (height h), the guy-wire represents the hypotenuse, and the horizontal distance from the base of the pole to the point where the wire is attached to the ground represents the base.
2. Identify the given values:
- The angle of elevation to the pole = 67 degrees.
- The distance from the base of the pole to the point where the wire is attached to the ground = 137 feet.
3. Identify the trigonometric relationship: In this case, we need to use the trigonometric function tangent (tan) because we know the angle and the lengths of the sides perpendicular (height h) and adjacent (base).
4. Write the trigonometric equation:
tan(67 degrees) = h / 137 feet
5. Solve for h: Now, we can rearrange the equation and solve for h:
h = 137 feet * tan(67 degrees)
6. Calculate the height: Use a calculator to find the value of tan(67 degrees) and multiply it by 137 feet to find the height h.
Note: Make sure your calculator is set to degree mode for accurate results.
By following these steps, you should be able to find the height of the pole.
km;k
Tangent problem of opp/adj
tan 67 degrees = x/137
Find tan of 67 and multiply by 137 to find the height of the pole.