Answer:
19.02 ft.
Step-by-step explanation:
Please find the attachment.
We have been given that a 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees.
We can see from our attachment that ladder forms a right triangle with building and ground.
The side of 20 ft is hypotenuse and side h is the opposite side to angle 72 degree.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(72^{\circ})=\frac{h}{20}[/tex]
Switch sides:
[tex]\frac{h}{20}=\text{sin}(72^{\circ})[/tex]
[tex]\frac{h}{20}*20=\text{sin}(72^{\circ})*20[/tex]
[tex]h=0.951056516295*20[/tex]
[tex]h=19.021130[/tex]
[tex]h\approx 19.02[/tex]
Therefore, the ladder would reach 19.02 feet high on the building.
A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees, The height of the ladder reach on the build will be 19.02 ft.
To find the height we will use Trigonometric formula.
Given : 20ft ladder leans against building and making [tex]72\textdegree[/tex]
As we can see in the diagram given below, when ladder leans to building it is making a right-angled triangle.
According to the figure, side p = 20 ft (height of ladder) that is the hypotenuse of the triangle and side is the perpendicular to angle 72 degree.
[tex]\rm \sin=\dfrac{perpendicular}{hypotenuse}\\\\\sin 72\textdegree= \dfrac{h}{20}\\\\\sin72\textdegree\times20=\dfrac{h}{20}\times20\\\\h=\sin 72\textdegree\times20\\\\\rm h= 0.951056516295\times20\\\\h= 19.021130\\\\h\approx 19.02[/tex]
Therefore, the height of the ladder will be 19.02 ft .
Learn more about Trigonometry here: https://brainly.com/question/8970167
