Question

In ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45. What is the value of the cosine of ∠X to the nearest hundredth?

Answer 1

The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

Step-by-step explanation:

The given is,

                   In ΔWXY, ∠Y=90°

                        XW = 53

                         YX = 28

                        WY = 45

Step:1

             Ref the attachment,

             Given triangle XWY is right angled triangle.

             Trigonometric ratio's,

                              $Cos$ ∅  $= \frac{Adj}{Hyp}$    

             For the given attachment, the trigonometric ratio becomes,

                              $Cos$ ∅  $= \frac{XY}{XW}$.....................................(1)

             Let, ∠X = ∅

             Where, XY = 28

                         XW =  53

             Equation (1) becomes,

                                 $Cos$ ∅  $= \frac{28}{53}$

                                 $Cos$ ∅ = 0.5283

                                        ∅ = $cos^{-1}$ (0.5283)

                                        ∅ = 58.109°

Result:

          The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.