A 16 m ladder is placed against the side of a house and reaches a window that is 12 m above the ground.1)How far from the base of the house is the ladder?(Round your answer to one decimal place and put only numbers in the blank with no units.)2) What is the angle of elevation of the ladder?(Round your answer to one decimal place and put only numbers in the blank with no units.)
Question
A 16 m ladder is placed against the side of a house and reaches a window that is 12 m above the ground.1)How far from the base of the house is the ladder?(Round your answer to one decimal place and put only numbers in the blank with no units.)2) What is the angle of elevation of the ladder?(Round your answer to one decimal place and put only numbers in the blank with no units.)
Solution
- To find the distance from the base of the house to the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, the height of the window is one side, and the distance from the base of the house to the ladder is the other side.
So, we have:
16^2 = 12^2 + x^2
256 = 144 + x^2
x^2 = 256 - 144
x^2 = 112
x = sqrt(112)
x = 10.6 (rounded to one decimal place)
So, the ladder is 10.6 m from the base of the house.
- To find the angle of elevation of the ladder, we can use the tangent function, which in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the angle of elevation is the angle at the base of the ladder, the height of the window is the side opposite the angle, and the distance from the base of the house to the ladder is the side adjacent to the angle.
So, we have:
tan(theta) = 12 / 10.6
theta = arctan(12 / 10.6)
theta = 48.4 degrees (rounded to one decimal place)
So, the angle of elevation of the ladder is 48.4 degrees.
Similar Questions
A 16 ft. ladder is leaning against a house. If the ladder reaches 12 ft. up the wall of the house, find the angle (to the nearest degree) that the ladder makes with the ground.
A ladder of 15 m length reaches a window of a house which is 12 m above the ground on one side of the street. Keeping the foot of the ladder at the same point it is turned to the other side of the street and now it reaches the window of some other house which is 9 m high. The width of street is :
A 7.4 m ladder is placed against a wall so that it forms a 68.7o angle with the ground. How far is the base of the ladder from the wall?(Round your answer to the nearest tenth and enter only the number with no units in the blank.)
2. A firefighter’s ladder leans against a building. If the ladder is 10 meters long and makes angle with the ground, and tan θ=3/8 ,a. how high up the building does the ladder reach?b. how far away is the foot of the ladder from the base of the building?
Colleen is helping decorate for homecoming week. She places the ladder against the wall at a safe angle. The ladder is 12 feet long and the base of the ladder is 3 feet away from the wall.What angle, in degrees, does the ladder make with the ground? Round to the nearest tenth. a bNone of these choices are correct. c dtan-1
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.