2 Trig Probs: height of balloon; height of mountain

[snakeyesxlaw]

If someone could just setup the diagram/picture for these two problems of what it looks like and the angle labels would be ideal, solving will be no problem afterward..

Problem #1)

A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles are found to be 14 degrees and 10 degrees. How high is the balloon?

The balloon is __________ above the ground.

Problem #2)
From a point A on a flat stretch near the base of a mountain the angle of elevation of Summit House at point C is 53.1 degrees. From a position B 950 feet farther away from the mountain, the angle of elevation to Summit House is 43.9 degrees.

What is the height h of the mountain?

 

[soroban]

Re: 2 Trig Problems

Hello, snakeyesxlaw!

If all you need are the diagrams, I can provide them.

1) A hot-air balloon is floating above a straight road.
To estimate their height above the ground, the balloonists simultaneously measure the angle
of depression to two consecutive mileposts on the road on the same side of the balloon.
The angles are found to be 14 degrees and 10 degrees. How high is the balloon?

    A *
      | *   *
      |   *       *
      |     *           * 
    y |       *               *
      |         *                   *
      |       14d *                 10d   *
      * - - - - - - * - - - - - - - - - - - - - *
      B      x      C           5280            D

The balloon is at A; the mile posts are C and D, 5280 feet apart.
The angles of depression are translated to ground-level angles.
. . \(\displaystyle \angle ADB = 10^o,\;\angle ACB = 14^o\)

I'll leave the rest up to you . . .

2) From a point A on a flat stretch near the base of a mountain the angle of elevation
of Summit House at point C is 53.1 degrees.
From a position B 950 feet farther away from the mountain, the angle of elevation
to Summit House is 43.9 degrees.
What is the height h of the mountain?

                                  * C
                              * * |
                          *   *   |
                      *     *     |
                  *       *       | h
              *         *         |
          * 43.9d     * 53.1d     |
      * - - - - - - * - - - - - - *
      B     950     A      x      D

Can you finish it now?