One end of a rope is tied to the top of a pole which is 30cm long and the rope is pulled tant then the other and is tied to a peg on the level ground.the angle of elevation which the rope makes with the ground is 55 degree celsius. Find the distance from the peg to the base of the pole?
The rope and pole form a rt. triangle
with the gnd. forming the hor. leg.
Tan A = Y/X = 30/X
Tan 55 = 30/X.
X = 30/Tan55 = 21 cm.
To find the distance from the peg to the base of the pole, you can use trigonometry. Let's break down the problem step by step.
1. Draw a diagram: Start by drawing a diagram of the situation described. Label the length of the pole as 30 cm and the angle of elevation as 55 degrees. Also, identify the distance from the peg to the base of the pole as 'd' (the value we need to find).
2. Identify the relevant trigonometric ratio: In this case, we can use the tangent ratio. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In our diagram, the opposite side is the height of the pole (30 cm) and the adjacent side is the distance 'd' from the peg to the base of the pole.
3. Use the tangent ratio to find 'd': The tangent of an angle can be found using a scientific calculator or by using the formula:
tangent(angle) = opposite/adjacent
Plugging in the values:
tangent(55 degrees) = 30 cm / 'd'
Now, solve for 'd':
'd' = 30 cm / tangent(55 degrees)
Using a scientific calculator, the tangent of 55 degrees is approximately 1.4281. Therefore:
'd' ≈ 30 cm / 1.4281
'd' ≈ 21.01 cm (rounded to two decimal places)
So, the distance from the peg to the base of the pole is approximately 21.01 cm.