A guy wire attached to the top of an electric pole makes a 70deg angle with the level ground. At a point 25 feet from the guy wire (farther away from the pole), the angel of elevation to the top of the pole is 42deg. How long is the guy wire?
In my sketch I see a non-rightangled triangle with angles
42° , 110° and 28°
with the side opposite the 42° as the guy wire
by the sine law:
x/sin42 = 25/sin28
x = 25sin42/sin28
= .....
To find the length of the guy wire, we can use trigonometric ratios. Let's break down the problem step by step:
Step 1: Draw a diagram
Sketch a diagram to visualize the situation. Draw the electric pole, the guy wire, the angle of inclination, and the distance from the point to the guy wire.
Step 2: Label the given information
In the diagram, label the angle of inclination between the guy wire and the ground as 70 degrees and the angle of elevation from the point to the top of the pole as 42 degrees. Also, mark the distance from the point to the guy wire as 25 feet.
Step 3: Identify relevant trigonometric ratios
In this problem, we can use the tangent ratio. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. For example, tan(α) = opposite/adjacent.
Step 4: Apply trigonometry
a. First, let's find the length of the side opposite the angle of elevation (42 degrees).
To do this, we can use the tangent ratio: tan(42°) = opposite/25 feet.
Rearranging the equation, we get opposite = tan(42°) * 25.
b. Next, let's find the length of the side opposite the angle of inclination (70 degrees).
Since this side represents the height of the pole, it must be the same length as the opposite side in step 4a. Therefore, we have the length of the opposite side, which is equal to the length of the guy wire.
Step 5: Calculate the length of the guy wire
Using the information from step 4b, the length of the guy wire is equal to the length of the opposite side, which we found to be: opposite = tan(42°) * 25 feet.
Now, you can calculate the length of the guy wire by plugging in the values into the equation and applying the multiplication:
length of guy wire = tan(42°) * 25 feet.