A 20-ft ladder is leaning against a building. If the base of the ladder is 7 ft from the base of the building,
what is the angle of elevation of the ladder? (Round your answer to one decimal place.)
How high does the ladder reach on the building? (Round your answer to the nearest whole number.)
Someone please hep me I tried everything and can you give me the final answer THank you
To find the angle of elevation of the ladder, we can use the inverse tangent function (tan^(-1)). The angle of elevation is the angle between the ladder and the ground.
First, let's draw a right triangle with the ladder as the hypotenuse (the longest side of the triangle), the distance from the base of the ladder to the building as the adjacent side, and the height of the building as the opposite side.
Using the Pythagorean theorem, we can calculate the height of the triangle:
height^2 + 7^2 = 20^2
height^2 + 49 = 400
height^2 = 351
height = √351
height ≈ 18.73 ft (rounded to two decimal places)
Now, to find the angle of elevation, we can apply the inverse tangent function:
angle = tan^(-1)(opposite/adjacent)
angle = tan^(-1)(18.73/7)
angle ≈ 69.6 degrees (rounded to one decimal place)
So, the angle of elevation of the ladder is approximately 69.6 degrees.
To calculate how high the ladder reaches on the building, we found the height of the triangle to be approximately 18.73 ft. Rounded to the nearest whole number, the ladder reaches about 19 ft on the building.
To find the angle of elevation of the ladder, we can use the trigonometric function tangent (tan).
The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height the ladder reaches on the building, and the adjacent side is the distance from the base of the ladder to the base of the building.
So, we have:
tan(angle) = opposite/adjacent
tan(angle) = height/7
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(height/7)
To find the height the ladder reaches on the building, we can use the Pythagorean theorem. The ladder, the base of the ladder, and the height on the building form a right triangle. The sum of the squares of the lengths of the two shorter sides (legs) of a right triangle is equal to the square of the length of the longest side (hypotenuse).
Using the Pythagorean theorem, we have:
hypotenuse^2 = height^2 + 7^2
Since we know the length of the hypotenuse (20 ft), we can solve for the height:
20^2 = height^2 + 7^2
400 = height^2 + 49
Subtracting 49 from both sides:
400 - 49 = height^2
351 = height^2
Taking the square root of both sides:
height = √351 ≈ 18.7 ft
So, the angle of elevation of the ladder is arctan(height/7) and the height the ladder reaches on the building is approximately 18.7 ft.
you did not try reviewing your basic trig functions and drawing a diagram.
Look at the diagram and you will see that
cosθ = 7/20
The height h can be found from θ, since
h/20 = sinθ
or, you can use the Pythagorean Theorem (have you forgotten that already?):
h^2+7^2 = 20^2