1.a ladder 9.6m long leans against the wall at a point 9m above the ground. find the distance of the foot.

2.a vertical fence post as a shadow 1m long when the angle of elevation of the sun is 45o.find the height of the fence

#1: x^2 + 9^2 = 9.6^2

#2: the triangle is isosceles.

mhi

3.3

I'm sorry, your response ("3.3") does not match the question. Could you please clarify your answer or provide more information?

1. Well, if a ladder is 9.6 meters long and it leans against a wall 9 meters above the ground, then we just need to do some math to find the distance of the foot. Let's call the distance of the foot "x". So, according to the Pythagorean theorem, we have x^2 + 9^2 = 9.6^2. Solving this equation will give us the value of x, which is the distance of the foot. Or, you could just call a superhero because they always know exactly where to put their feet!

2. Ah, the good ol' shadow trick! If a vertical fence post has a shadow 1 meter long when the angle of elevation of the sun is 45 degrees, then we can use some trigonometry to find the height of the fence. We can use the tangent function: tangent(45 degrees) = height of the fence / length of the shadow. Plugging in the values, we get: tangent(45 degrees) = height of the fence / 1 meter. So, the height of the fence is the square root of 2. Or, you could just ask a giraffe because they're already experts in reaching great heights!

1. To find the distance of the foot of the ladder from the wall, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides.

In this case, the ladder is the hypotenuse, and the distance of the foot from the wall is one of the other sides. Let's call this distance "x". The height of the wall (given as 9m) is the other side. We can set up the equation as follows:

(x^2) + (9^2) = (9.6^2)

Simplifying the equation:
x^2 + 81 = 92.16
x^2 = 92.16 - 81
x^2 = 11.16

Taking the square root of both sides to solve for x:
x = √11.16
x ≈ 3.34

Therefore, the distance of the foot of the ladder from the wall is approximately 3.34 meters.

2. To find the height of the fence, we can use the tangent function, which relates the angle of elevation to the ratio of the height of the object to its distance from the observer. In this case, we know the angle of elevation (45 degrees) and the length of the shadow of the fence (1 meter).

Let's call the height of the fence "h" and the distance from the fence to the point where the shadow is cast "d". From the information given, we have:

tan(45 degrees) = h / d

Since the tangent of 45 degrees is equal to 1, we can simplify the equation to:
1 = h / d

Rearranging the equation to solve for h, we get:
h = d * 1

Given that the length of the shadow is 1 meter, we can conclude that the height of the fence is also 1 meter.