Pre-Calculus Trigonometry

[ambright4ever]

From a point A that is 10 meters above level ground, the angle of elevation of the top of a building is 42 degrees and the angle of depression of the base of the building is 8 degrees. Approximate the height of the building.

Can someone please help me with this!? I would greatly appreciate it! Thanks in advance!

 

[tkhunny]

Did you draw a picture?

Draw a 10 m tower with a much taller building some distance away. (Exactly where and how you draw these relationships CAN help you or confuse you. It's not particularly important to get it perfect on the first try. Feel free to draw things from a blank slate if you find something isn't making sense. For example, the other building MUST be taller than 10 m or you cannot get an Angle of Elevation. So, make sure it's taller.)

Climb to the 10 m roof and walk toward the taller building until you are standing right on the edge. (Please hold the hand rail!)

Now, draw three lines.

1) From your toes at exactly 10 m off the ground, draw a horizontal line toward the other building. This is your horizon or reference line.
2) Again from your toes, draw a line ABOVE the reference line to the top of the other building. Label the Angle of Elevation as indicated in the problem statement.
3) Again from your toes, draw a line BELOW the reference line to the bottpm of the other building. Label the Angle of Depression as indicated in the problem statement.

Where does that leave us?

 

[soroban]

Hello, ambright4ever!

From a point A that is 10 meters above level ground,
the angle of elevation of the top of a building is $\displaystyle 42^o$
and the angle of depression of the base of the building is $\displaystyle 8^o.$
Approximate the height of the building.

Here is a diagram. .(d = degrees)

                              * C
                           *  |
                        *     |
                     *        | y
                  *           |
               *              |
            *                 |
         * 42d      x         |
    A * - - - - - - - - - - - * D
      |     *   8d            |
   10 |           *           | 10
      |                 *     |
    B * - - - - - - - - - - - * E

Here is a game plan . . .

In $\displaystyle \Delta ADE\!:\;\tan8^o \,=\,\frac{10}{x} \quad\Rightarrow\quad x \,=\,\frac{10}{\tan8^o}$

In $\displaystyle \Delta CDA\!:\;\tan42^o \,=\,\frac{y}{x} \quad\Rightarrow\quad y \,=\,x\tan42^o$

Therefore: .$\displaystyle CE \:=\:y + 10$

 

[ambright4ever]

Omg! Thank you all so much! Ya'll was wonderful help! :grin: