Trigonometry Problem ( Can Anyone Help Me PLEASE )?

Question

This is the question:

CD is a vertical pole with the height of 10m. Which stands with it's bottom C on horizontal ground. A and B are two points on the ground on the same side of C and in line with C. From the top D of the flagpole the angles of depression of A and B are 20 degrees and 50 degrees respectively.

(i) show that AC= 10/tan 20° m and BC= 10/tan50° m.

(ii)find the exact length of AB

(iii)find the length of AB correct to the nearest cm

guys any help would be appreciated

please i just dont really get this question.

thanks in advance :D

Answer 1

Have you drawn a sketch of the situation?

No?

I suggest you do that.

It's about trigonometry and solving triangles.

I hope that helps.

Answer 2

< DAC = 20 degrees

<DBC = 50 degrees.

i) imagine right triangle DCA.

tan<DAC = CD / AC

tan 20 = 10 / AC

AC = 10 / tan20.

imagine right triangle DCB.

tan<DCB = CD / BC

tan 50 = 10 / BC

BC = 10 / tan 50.

ii) AB = AC - BC

        = 10/tan20 - 10 / tan50

        = 10 ( 1/tan20 - 1/tan50 )

        = 10 ( tan50 - tan20) / tan50*tan20.

iii) evaluating the above expression using a calculator, we get

AB = 19.084 m

     = 190.84 cm

     =191 cm (approx.).