A boy 1.2m tall stands 6m away from the foot of a vertical land pole 4.2m long. If the land is at the top of the pole,(a)represent this information in a diagram (b)calculate the (I)length of the shadow of the boy cast by the land (ii)angle of elevation of the land from the boy,correct to the nearest degree

(a) To represent this information in a diagram, we can draw a vertical line to represent the pole. At the top of the pole, we can draw a small triangle to represent the land. Next, we draw another line from the bottom of the pole to represent the height of the boy. Finally, we extend a line from the top of the boy's height to represent the shadow cast by the land. It should look something like this:

```
|\
| \
| \
| \
| \
|______\
pole
```

(b) To calculate the length of the shadow of the boy cast by the land, we can use similar triangles. The corresponding sides of similar triangles are proportional, so we can set up the following ratio:

(Shadow length)/(Boy height) = (Distance from boy to pole)/(Length of pole)

Let's substitute the given values into the equation:

(Shadow length)/(1.2) = (6)/(4.2)

Cross-multiply and solve for the shadow length:

Shadow length = (1.2 * 6) / 4.2 = 7.2 / 4.2 ≈ 1.7143 meters

Therefore, the length of the shadow of the boy cast by the land is approximately 1.7143 meters.

To calculate the angle of elevation of the land from the boy, we can use trigonometry. The angle of elevation is the angle between the ground and the line connecting the boy's eye level to the top of the pole.

Let's label the angle we're trying to calculate as "θ". Then, we can use the tangent function:

tan(θ) = (Length of pole)/(Distance from boy to pole)

We have the values, so we can plug them in:

tan(θ) = 4.2 / 6

Using inverse tangent (arctan or tan^(-1)), we can find the angle:

θ = arctan(4.2 / 6)

Using a calculator, we find that θ ≈ 33.69 degrees.

Therefore, the angle of elevation of the land from the boy, correct to the nearest degree, is approximately 34 degrees.