Thread: Trig Ratios Right Triangles

I was doing some homework in my math book and I'm having a hard time with these questions. Here is one that i don't have much idea to do with. Grade 11 University math thanks!

Question 1:
The arm of a boom crane is 12m long. Because of the location of the construction site, the angle of inclination of the boom of the crane has a minimum value of 30 degrees and a maximum of 45 degrees. Find the vertical displacement of the end of the boom as
a) an exact value
b) an approximate value, to the nearest tenth of a metre.

Hello, Sarah!

1) The arm of a boom crane is 12m long.
Because of the location of the construction site, the angle of inclination
of the boom of the crane has a minimum value of 30° and a maximum of 45°.

Find the vertical displacement of the end of the boom as
a) an exact value
b) an approximate value, to the nearest tenth of a metre.

Code:

                        *
                     *  |
             12   *     |
               *        | y1
            *           |
         * 30°          |
      * - - - - - - - - *

You're expected to the ratio of the sides of a 30-60 right triangle.

The side opposite the 30°-angle is always one-half the hypotenuse.

Hence: . m.

Code:

                  *
                * |
          12  *   |
            *     | y2
          *       |
        * 45°     |
      * - - - - - *

You should know that sides of a 45-45 right triangle are in the ratio: .

Hence: .


Therefore: .

. . . . . . . .


.