A ladder leaning against a house makes an angle of 60 degrees. The foot of the ladder is 7 feet from the house. How long is the ladder and what would the situtaion look like as a right triangle?
sin60 = 7/L. L = Length of ladder.
L is also the hypotenuse of a right triangle.
actually, cos60 = 7/L
Oops. Henry is right if the angle with the wall is 60
To solve this problem, we can use trigonometric functions, specifically the sine function.
1. Let's assume the height of the ladder, which is opposite to the angle of 60 degrees, is 'h'.
2. The length of the base of the triangle, which is the distance from the foot of the ladder to the house, is given as 7 feet. This is the adjacent side to the angle of 60 degrees.
3. Now, we can use the sine function to relate the opposite side and the hypotenuse of the right triangle:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = h/l
4. The sine of 60 degrees is √3/2, so we can substitute it into the equation:
√3/2 = h/l
5. To solve for 'h', we can rearrange the equation:
h = (√3/2) * l
6. We know that the distance from the foot of the ladder to the house is 7 feet, so we substitute it into the equation:
7 = (√3/2) * l
7. Now we can solve for 'l', the length of the ladder:
l = 7 / (√3/2)
l = 7 * (2/√3)
l = (14√3)/3
l ≈ 8.08 feet (rounded to two decimal places)
So, the length of the ladder is approximately 8.08 feet.
In the right triangle situation, the ladder forms the hypotenuse, the distance from the foot of the ladder to the house forms the base, and the height of the ladder forms the perpendicular side of the right triangle.
check your 30-60-90 right triangle. Its sides are in the ratio
1:√3:2
You have the short side = 7, so scale it up.