a ladder leaning against a wall makes a 60 degree angle with the ground. the base of the ladder is 4m from the building. how high above the ground is the top of the ladder?
problem im on online schooling and its a special right triangles assignment and i don't have a calculator do to tangent and all that so that's why i need help.
You should really get yourself a scientific calculator.
You can now get them around $10, I have seen them sell at about $5
Secondly you should memorize the ratio of sides of the standard 30-6-90 and the 45-45-90 right-angled triangles, in this case this is what they probably expected
the sides opposite the 30-60-90 are 1 , √3, 2
and for the 45-45-90 the sides are 1, 1, √2
so tan 60 = √3/1
=1.7321
so height = 4(1.7321) = 6.93 appr
short leg = 4; to find long leg multiply 4 x 2; long leg = 8; to find how high; use x^2 + 4^2 = 8^2
so: x^2 + 16 = 64; subtract 16 from both sides: x^2 = 48; find the square root of 48; x = 6.93 so the top of the ladder is 6.93 m above the ground.
Why did the ladder start dating the wall? Because they had amazing chemistry and were always on the same level! Now, let's solve your problem and find out how high above the ground the top of the ladder is.
Given that the ladder is forming a 60-degree angle with the ground and the base is 4m from the building, we can use some trigonometry to find the height.
Since the ladder forms a right triangle with the ground and the wall, we can use the sine function. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
In this case, the opposite side is the height above the ground, and the hypotenuse is the length of the ladder. So, we have:
sin(60°) = height / length of the ladder
Simplifying, we find:
height = length of the ladder * sin(60°)
Since we know the base of the ladder is 4m, the length of the ladder is the hypotenuse of the right triangle, which is also the same as the distance between the ground and the top of the ladder. So:
height = 4m * sin(60°)
Plugging in the values, we get:
height = 4m * 0.866
Solving that, we find:
height ≈ 3.464m
So, the top of the ladder is approximately 3.464 meters above the ground.
To solve this problem, we can use trigonometry, specifically the sine function. Let's call the height of the ladder "h" (which is what we want to find) and the length of the ladder "L".
In a right triangle formed by the ladder, the distance from the base of the ladder to the wall (4m) is the adjacent side of the angle, and the height of the ladder (h) is the opposite side. The ladder itself is the hypotenuse.
Since we're given the angle (60 degrees) and the adjacent side (4m), we can use the sine function to find the height (opposite side).
The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the equation becomes:
sin(60 degrees) = h / L
To solve for "h", we need to find "L".
Using the Pythagorean theorem, we know that the hypotenuse (L) squared is equal to the sum of the squares of the other two sides:
L^2 = 4^2 + h^2
L^2 = 16 + h^2
Now, we can substitute this expression for L^2 in the sine function equation:
sin(60 degrees) = h / √(16 + h^2)
The sine of 60 degrees is √3/2, so the equation becomes:
√3/2 = h / √(16 + h^2)
To simplify the equation, we can multiply both sides by √(16 + h^2):
√3√(16 + h^2)/2 = h
Now, let's square both sides to eliminate the square roots:
(3√(16 + h^2))^2 / 4 = h^2
(48 + 3h^2) / 4 = h^2
48 + 3h^2 = 4h^2
48 = h^2
Taking the square root of both sides, we find:
h = √48
Simplifying the square root of 48, we get:
h ≈ 6.93 meters
So, the height above the ground of the top of the ladder is approximately 6.93 meters.
tan 60° = height/4
height = 4tan60 = .....