Question

A ladder leans against a building, making a 63 angle of elevation with the ground.The top of the ladder reaches a point on the building that is 37 feet above theground. To the nearest tenth of a foot, what is the distance between the base of the building and the base of the ladder? Use the correct abbreviation for the units.If the answer does not have a tenths place then include a zero so that it does.

Answer 1

- To better understand the problem, we can make a sketch as follows:

- The above figure depicts what was described by the question.

- We are asked to find the distance between the base of the ladder and the base of the building, and we have labeled it as x.

- To find the value of x, we simply apply SOHCAHTOA.

- That is,

`\begin{gathered} \tan\theta=(Opposite)/(Adjacent) \\ \\ \tan63\degree=(37)/(x) \\ \\ \text{ Rewrite,} \\ \\ x=(37)/(\tan63\degree) \\ \\ \therefore x=18.852441...\approx18.9\text{ \lparen TO THE NEAREST TENTH OF A FOOT\rparen} \end{gathered}`

Final Answer

The distance of the base of the building from the base of the ladder is 18.9 feet.