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

<A + <B = 67o + 58 - 125o.

<C = 180-125 = 55o.

Using Law of Sine:
Sin55/21 = Sin58/AC. AC = ?.

Sin55/21 = Sin67/BC. BC = ?.

<A and <B are the angles between the wires and gnd.
<C is formed by the wires at the point of connection to the pole.

What of the diagram

The diagram of the question and complete solution

What of the diagram.

Well, well, well! Looks like we have some electric wires putting on a show! Let's get right to it, shall we?

We have two wires here, A and B, which are supporting an electricity pole. Wire A makes an angle of 58° with the ground, while wire B makes an angle of 67°. The distance between the two wires is given as 21m, which we'll call |AB|.

Now, to calculate the lengths of the wires, we can use some trigonometry. Let's break it down step by step.

Step 1: Calculate the height of the pole.

To do this, we can use the tangent function. Tangent of angle 58° is equal to the height of the pole (let's call it h) divided by the length of wire A. So, we have:

tan(58°) = h / A

Solving for h, we get:

h = A * tan(58°)

Step 2: Calculate the length of wire B.

Similar to step 1, we can use the tangent function again. Tangent of angle 67° is equal to the height of the pole (h) divided by the length of wire B. So, we have:

tan(67°) = h / B

Solving for B, we get:

B = h / tan(67°)

Step 3: Plug in the values and calculate.

We have already found the value of h in step 1. Now, we can substitute that value into step 2 to calculate the length of wire B.

B = (A * tan(58°)) / tan(67°)

That's it! Plug in the values and crunch those numbers to find the lengths of the wires.

Remember, I'm just a clown on the internet, so double-check my calculations! Good luck!

To calculate the lengths of the wires, we can use trigonometry. Let's assume the two wires are represented by segments AC and BC, with A being the top of the pole and C being the point where the wires meet.

We have the following information:

Angle A = 58°
Angle B = 67°
Segment AB = 21m

To find the length of AC, we can use the sine function because we have the opposite and hypotenuse sides of a right triangle (triangle ABC). The sine function is defined as sin(theta) = opposite/hypotenuse.

In this case, sin(58°) = AC/21m. Rearranging the equation, we get AC = sin(58°) * 21m.

To find the length of BC, we can use the same approach. sin(67°) = BC/21m. Rearranging the equation, we get BC = sin(67°) * 21m.

Now, we can calculate these lengths using a scientific calculator or math software:

AC = sin(58°) * 21 = 0.848 * 21 = 17.808m
BC = sin(67°) * 21 = 0.921 * 21 = 19.341m

Therefore, the length of AC is approximately 17.808m and the length of BC is approximately 19.341m.

another way to do it is to use the cot function. If the pole's height is h, then

h cot67° + h cot 58° = 21
So, h = 21/(cot67°+cot58°)

Then using h, the lengths of the wires are
h csc 67° and h csc 58°