Question

A ladder leans against a building, making a 72 angle of elevation with the ground.The top of the ladder reaches a point on the building that is 27 feet above theground. To the nearest tenth ofa foot, what is the distance between the base of thebuilding and the base of the ladder? Use the correct abbreviation for the units. If theanswer does not have a tenths place then include a zero so that it does.

Answer 1

Let us make a diagram to represent the information.

From the diagram above, we can see how the ladder made the angle 72 degrees elevation. This has made a right-triangle which can be seen at the right side. Using the right-triangle, we would be finding the side d.

From the trig-ratio SOHCAHTOA, we have that

`\begin{gathered} SOHsin\theta=(opposite)/(hypotenuse) \\ CAHcos\theta=(adjacent)/(hypotenuse) \\ TOAtan\theta=(opposite)/(adjacent) \end{gathered}`

From the right triangle I have made,

`\begin{gathered} \theta\text{ means the acute angle 72}\degree \\ opposite\text{ is the side of the triangle opposite 72}\degree=27\text{ feet} \\ adjacent\text{ is the side that has the acute angle and 90}\degree,\text{ this is d} \end{gathered}`

So we will make use of TOA, since the longest side which is hypotenuse is not given, so we have

`\begin{gathered} TOAtan\theta=(opposite)/(adjacent) \\ tan72\degree=(27)/(d) \\ cross\text{ multiplying } \\ tan72\degree* d=27 \\ tan72d=27 \\ dividing\text{ both sides by tan 27, we have } \\ d=(27)/(tan72\degree) \\ d=(27)/(3.07768) \\ d=8.77283 \\ d=8.8\text{ } \end{gathered}`

Hence the answer is 8.8 feet to the nearest tenth