A 35-foot long ladder is leaning against the wall of a building.How far from the ground is the top of the ladder and how far from the base of the building is its foot if it makes a 20 degrees angle with the wall?
The top is =35 cos 20 degrees
the foot is =35 sin 20 degrees
To find the height of the ladder, we can use the sine ratio of a right triangle. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Given that the ladder is leaning against the wall at a 20 degree angle, and the length of the ladder is 35 feet, we can set up the equation as follows:
sin(20 degrees) = height of ladder / length of ladder
Rearranging the equation, we get:
height of ladder = sin(20 degrees) * length of ladder
Calculating the height of the ladder:
height of ladder = sin(20 degrees) * 35 feet
Using a calculator, we find that sin(20 degrees) is approximately 0.3420.
height of ladder = 0.3420 * 35 feet
height of ladder = 11.97 feet (rounded to two decimal places)
Therefore, the top of the ladder is approximately 11.97 feet from the ground.
To find the distance from the base of the building to the foot of the ladder, we can use the cosine ratio of a right triangle. The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Given that the ladder is leaning against the wall at a 20 degree angle, and the length of the ladder is 35 feet, we can set up the equation as follows:
cos(20 degrees) = distance from base to foot / length of ladder
Rearranging the equation, we get:
distance from base to foot = cos(20 degrees) * length of ladder
Calculating the distance from base to foot:
distance from base to foot = cos(20 degrees) * 35 feet
Using a calculator, we find that cos(20 degrees) is approximately 0.9397.
distance from base to foot = 0.9397 * 35 feet
distance from base to foot = 32.79 feet (rounded to two decimal places)
Therefore, the foot of the ladder is approximately 32.79 feet from the base of the building.
To find the distance from the ground to the top of the ladder and the distance from the base of the building to the foot of the ladder, we can use trigonometry.
Let's call the distance from the ground to the top of the ladder 'h', and the distance from the base of the building to the foot of the ladder 'd'. We are given that the ladder makes a 20-degree angle with the wall.
We can use the sine trigonometric function to find the value of 'h'. The sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, the length of the side opposite the angle is 'h', and the hypotenuse is the length of the ladder, which is 35 feet.
So we have: sin(20 degrees) = h / 35
To find the value of 'h', we can rearrange the equation:
h = sin(20 degrees) * 35
Using a calculator, we can find that sin(20 degrees) is approximately 0.3420. So, we have:
h = 0.3420 * 35
h ≈ 11.97 feet
Therefore, the distance from the ground to the top of the ladder is approximately 11.97 feet.
To find the distance from the base of the building to the foot of the ladder, we can use the cosine trigonometric function. The cosine of an angle is equal to the length of the side adjacent to the angle divided by the hypotenuse.
So we have: cos(20 degrees) = d / 35
To find the value of 'd', we can rearrange the equation:
d = cos(20 degrees) * 35
Using a calculator, we can find that cos(20 degrees) is approximately 0.9397. So, we have:
d = 0.9397 * 35
d ≈ 32.79 feet
Therefore, the distance from the base of the building to the foot of the ladder is approximately 32.79 feet.