Question

Help pleaseeeeeeeeee​

Answer 1

Answer: Area of Δ DUO = 12.0 square units.

Step-by-step explanation:

From the diagram, Δ DPA is a right angled triangle and right angled at P.

Therefore ∠D will be

Tan ∅° = PA/DP ie, opposite side all over the adjacent.

            = 4.5/3.75

Tan∅°   = 1.2

to calculate ∅°, we know find the inverse of Tan 1.2

∅ = Tan^-1 1 .2 from your log tables or calculator

         ∅° = 50.20°.

               = 50°

Since line DR is ⊥ to line OP

∠ADR = 90° - 50°

            = 40°.

From the diagram,

     ∠ADR = ∠UDR = 40°

Therefore,

    ∠ODU = 180 - ( 40 + 40 + 90 )  { Angle on a straight line }

                 = 180 - 170

                 = 10°

From Δ UDM , line MU is he height of the required Δ DUO whose area is to be determined.

Now find the height MU

            Tan10.0° = MU/10, where MU is the opposite side and 10.0 is the adjacent from the diagram given.

             MU = Tan10.0 x 10.0

                    =  0.1763 x 10.0

                    =  1.763

Therefore to calculate the area of Δ DUO

                    =   1/2 x base x height

                    = 1/2 x line OD x line MU

                    = 1/2 x 14.0 x 1.763

                    = 7 x 1.763

                    = 12.341

                    = 12.0 square units.

         

           =