SIN COS TAN I REALLY NEED HELP FAST.

[DVSLITTLEONE1]

From the parking lot at the Red Hill Shopping Center, the angle of sight (elevation) to the top of the hill is about 25. From the base of the hill you can also sight the top but at an angle of 55. The horizontal distance between sightings is 740 feet. How high is Red Hill? Show your subproblems.

i HAVE DONE THIS SO FAR...

740(TAN25) = 0.4663

I AM STILL UNSURE IF IM DOING THIS RIGHT. IM REALLY CONFUSED

 

[Gene]

First you need a picture. The distance from the foot of the hill to a spot under the top is d. The height is h.

                /|A 
               / |
              /  |h
             /   |
            /    |
 D_________C_____B
    740       d

The hill is CA, parking lot is D, the hilltop is A, B is directly under it. Angle CDA = 25. Angle BCA = 55. Write the tangent equations of the two right triangles ABD and ABC. Solve the ABC triangle for d then substitute that in the ABD tan equation.

 

[soroban]

Hello, DVSLITTLEONE1!

From the parking lot at the Red Hill Shopping Center,
the angle of sight (elevation) to the top of the hill is about 25°.
From the base of the hill you can also sight the top but at an angle of 55°.
The horizontal distance between sightings is 740 feet.
How high is Red Hill? Show your subproblems.[/color]

i HAVE DONE THIS SO FAR... 740(TAN25) = 0.4663 \(\displaystyle \;\)??

I AM STILL UNSURE IF IM DOING THIS RIGHT. \(\displaystyle \;\) . . . doing what right?

                      *A
                    //:
                  / / :
                /  /  :
              /   /   :h
            /    /    :
          /     /     :
        /25°   /55°   :
      * - - - * - - - +
      D  740  C   d   B

Gene gave you an excellent game plan . . .

In right triangle ABC, we have: \(\displaystyle \,\tan55^o\,=\,\frac{h}{d}\;\;\Rightarrow\;\;h\,=\,d\cdot\tan55^o\;\) [1]

In right triangle ABD, we have: \(\displaystyle \,\tan25^o\,=\,\frac{h}{d\,+\,740}\;\;\Rightarrow\;\;h\,=\,(d\,+\,740)\cdot\tan25^o\;\) [2]

Equate [1] and [2] and solve for \(\displaystyle d\).

Substitute into [1] and solve for \(\displaystyle h\).

 

[DVSLITTLEONE1]

thanks for the help. it helped haha