A flagstaff is placed one corner of a level rectangular playground 40m and 30m wide. If the angle of elevation of the top of the flagstaff from the opposite corner of the ground is 45°.calculate the height of the flagstaff.

Can I know the figure plz

Distance between two opposite points on the ground:

= root(l^2 + b^2)
= root(40^2 + 30^2)
= root(1600 + 900)
= root(2500) = 50m

If θ is the angle of elevation, then:
tanθ = Height of flag/Distance between opposite points
=> tan(45) = h/50
=> 1 = h/50
=> h = 50m

To find the height of the flagstaff, we can use trigonometry and the given information about the angle of elevation. Let's go step by step:

Step 1: Draw a diagram of the rectangular playground. Label the length as 40m and the width as 30m. Place the flagstaff at one corner of the rectangular playground.

Step 2: From the opposite corner of the ground, draw a straight line to the top of the flagstaff. This line represents the line of sight from the observer to the top of the flagstaff.

Step 3: Since the angle of elevation is 45°, draw a horizontal line from the opposite corner of the ground to meet the line of sight.

Step 4: Now, we have a right triangle. The horizontal line represents the base of the triangle, which is 30m. The line of sight represents the hypotenuse, and the height of the flagstaff represents the opposite side of the right triangle.

Step 5: Since we have the adjacent side (30m) and the hypotenuse (line of sight), we can use the tangent function to find the height of the flagstaff.

Step 6: The tangent of an angle can be calculated as: tan(angle) = opposite/adjacent. In this case, tan(45°) = height of flagstaff/30.

Step 7: Solve the equation for the height of the flagstaff:
tan(45°) = height of flagstaff/30
1 = height of flagstaff/30
height of flagstaff = 30 meters

Therefore, the height of the flagstaff is 30 meters.

To calculate the height of the flagstaff, we can use trigonometry.

First, let's draw a diagram to visualize the problem.

```
A
|\
| \
| \
| \ h (height of flagstaff)
| \
| \
| \
|______\
B d C
```

In the diagram, A represents the top of the flagstaff, B represents one corner of the playground, and C represents the opposite corner from where we are observing the flagstaff. The distance BC is given as 40m, and the distance AC is given as 30m. The angle of elevation, ABC, is given as 45°.

Now, let's break down the problem.

We can use the tangent function, which relates the angle of elevation to the height and distance.

Tangent of the angle ABC = height (h) / base (d)

In this case, the base (d) is the distance AB. To find AB, we can use the Pythagorean theorem:

AB^2 = AC^2 + BC^2

Substituting the given values:

AB^2 = (30m)^2 + (40m)^2
AB^2 = 900m^2 + 1600m^2
AB^2 = 2500m^2
AB = √2500m^2
AB = 50m

Now, we can use the tangent function to find the height (h):

tan(45°) = h / 50m

Simplifying the equation:

1 = h / 50m
h = 50m

Therefore, the height of the flagstaff is 50m.

In summary, we used trigonometry to calculate the height of the flagstaff. We first found the length of the base (AB) using the Pythagorean theorem, and then used the tangent function to determine the height (h) based on the given angle of elevation (45°).