A pole 7 meters long is placed against a wall at an angle of 45 degrees, what is the height of the wall
since the angle is 45º, you have an isosceles right-angled triangle
so 7 is the hypotenuse and each of the other two sides can be called x
x^2 + x^2 = 7^2
2x^2 = 49
x^2 = 24.5
x = √24.5 = approx. 4.95 m
OR
sin 45º = height of wall/7
height of wall = 7sin45º
= 7(.7071067)
= appr. 4.95 m
If the top of the pole (of length L) rests on the top of the wall, the wall height H is such that
sin 45 = H/L = (sqrt2)/2
Solve for H
Use a trig function that states
opposite/hypotenuse.
Of course, this would be the sine function.
sin(45degrees) = h/7meters
Let h = height of building
sin45 = h/7
sin45 times 7 = h
4.949747468 = h
Round 4.949747468 to the nearest tenths becomes 4.95 meters.
The height of the building is about
4.95 meters in height.
To find the height of the wall, we can use trigonometry.
In this case, we are dealing with a right-angled triangle formed by the pole, the wall, and the ground. The angle between the pole and the ground is 45 degrees.
The length of the pole is the hypotenuse of the triangle, and the height of the wall is the side opposite the 45-degree angle.
To find the height of the wall, we can use the trigonometric function tangent (tan). In this case, tangent is defined as the ratio of the length of the side opposite to an angle to the adjacent side.
The formula is:
tan(theta) = opposite / adjacent
In this case, theta is the 45-degree angle, opposite is the height of the wall, and adjacent is the length of the pole.
We can rearrange the formula to solve for the height:
opposite = adjacent * tan(theta)
Given that the length of the pole is 7 meters, we can calculate the height:
height = 7 * tan(45 degrees)
Using a scientific calculator, we can calculate the value of tan(45 degrees):
tan(45 degrees) ≈ 1
Now we can substitute the values into the formula:
height ≈ 7 * 1
Therefore, the height of the wall is approximately 7 meters.