tylers 14 foot ladder makes a 62 degree angle with the ground.To the nearest foot, how far up the house does tylers ladder reach, and how far away from the house is the base of the ladder
height --- h
base --- b
sin62 = h/14
h = 14sin62° = ...
cos62° = b/14
b = 14cos62 = ....
To find out how far up the house Tyler's ladder reaches, and how far away from the house the base of the ladder is, we can use trigonometry.
Let's consider the ladder as the hypotenuse of a right triangle, with one angle of 62 degrees. The height of the ladder reaching up the house will be the opposite side, and the distance from the house to the base of the ladder will be the adjacent side.
Now, we can use the trigonometric functions sine and cosine to calculate the values we need.
First, let's find the height of the ladder using the sine function:
sin(angle) = opposite / hypotenuse
sin(62 degrees) = height of ladder / 14 feet
height of ladder = sin(62 degrees) * 14 feet
height of ladder ≈ 11.99 feet ≈ 12 feet (to the nearest foot)
Next, let's find the distance from the house to the base of the ladder using the cosine function:
cos(angle) = adjacent / hypotenuse
cos(62 degrees) = distance from house / 14 feet
distance from house = cos(62 degrees) * 14 feet
distance from house ≈ 6.17 feet ≈ 6 feet (to the nearest foot)
Therefore, Tyler's ladder reaches approximately 12 feet up the house, and the base of the ladder is approximately 6 feet away from the house.
To determine how far up the house Tyler's ladder reaches and how far away from the house the base of the ladder is, we can use trigonometry.
Let's label the height(up the house) as "h" and the distance from the house(base) as "d".
We know that the ladder forms a 62-degree angle with the ground. This angle is between the ladder and the ground, so we can say it is the angle opposite the height "h".
Using trigonometry, we can use the sine function:
sin(angle) = opposite/hypotenuse
In this case, the height "h" is the opposite side, and the hypotenuse is the ladder length, which is 14 feet.
sin(62°) = h/14
To solve for "h", we can rearrange the equation:
h = sin(62°) * 14
Calculating this value, h ≈ 12.41 feet.
Therefore, to the nearest foot, Tyler's ladder reaches approximately 12 feet up the house.
To find the horizontal distance "d" from the house(base), we can use the cosine function:
cos(angle) = adjacent/hypotenuse
In this case, the distance "d" is the adjacent side, and the hypotenuse is still the ladder length of 14 feet.
cos(62°) = d/14
To solve for "d", we can rearrange the equation:
d = cos(62°) * 14
Calculating this value, d ≈ 6.33 feet.
Therefore, to the nearest foot, the base of Tyler's ladder is approximately 6 feet away from the house.