AB is a 6 m high pole. CD is a ladder inclined at an angle of 60 degrees to the horizontal and reaches up to a point D of the pole. If AD = 2.54 m, find the length of the ladder
sin60 = AD/CD = 2.54/CD. CD = ?.
To find the length of the ladder, we can use trigonometry. Let's break down the problem step by step:
1. Visualize the problem:
Draw a triangle ABC, where A is the top of the pole, B is the bottom of the pole, and C is the foot of the ladder on the ground. Angle ACD is 60 degrees as given in the problem.
```
A
/|
/ |
/ |
D /_____| C
B
```
2. Identify the known values:
We know that AB is the height of the pole and it is given as 6 meters. We also know that AD is given as 2.54 meters.
3. Identify the unknown values:
We need to find the length of the ladder, which is AC or CD.
4. Use trigonometry to find the missing length:
In right triangle ACD, we have the adjacent side (AD) and we need to find the hypotenuse (AC or CD).
Using the cosine ratio, we have:
cosine(angle) = adjacent/hypotenuse
cos(60 degrees) = AD/AC
Rearranging the equation, we get:
AC = AD/cos(60 degrees)
5. Substitute the known values and calculate:
AC = 2.54 meters / cos(60 degrees)
Calculating the value of cos(60 degrees), we get:
AC = 2.54 meters / 0.5
AC = 5.08 meters
So, the length of the ladder (AC or CD) is 5.08 meters.