Question

Please help. Find the length of the side labeled x. Round intermediate values ​​to the nearest thousandth. Use the rounded values ​​to value. Round your final answer to the nearest tenth

Answer 1

19)18.7 20)7.9
21)13.3 22)102.4

Answer 2

18.692

48.344

7.075

101.972

Explanation:

19)

`cos23=(BD)/(AB)\\\Rightarrow BD=cos23* 29`

`tan 55=(BD)/(DC)\\\Rightarrow tan 55=(cos23* 29)/(x)\\\Rightarrow x=(cos23* 29)/(tan55)\\\Rightarrow x=18.692`

x = 18.692

20)

`tan68=(AD)/(BD)\\\Righarrow tan68=(16)/(BD)\\\Rightarrow BD=(16)/(tan68)`

`cos35=(BD)/(BC)\\\Rightarrow cos35=((16)/(tan68))/(x)\\\Rightarrow x=((16)/(tan68))/(cos35)\\\Rightarrow x=48.344`

x = 48.344

21)

`cos62=(BD)/(AB)\\\Rightarrow cos62=(BD)/(20)\\\Rightarrow BD=20* cos62`

`tan 37=(DC)/(BD)\\\Rightarrow tan 37=(x)/(20* cos62)\\\Rightarrow x=tan37* 20* cos62\\\Rightarrow x=7.075`

x = 7.075

22)

`tan24=(AD)/(BD)\\\Rightarrow tan24=(47)/(BD)\\\Rightarrow BD=(47)/(tan24)`

`tan44=(DC)/(BD)\\\Rightarrow tan44=(x)/((47)/(tan24))\\\Rightarrow x=tan44* (47)/(tan24)\\\Rightarrow x=101.972`

x = 101.972

A, B, C and D have been taken according to the diagram for all the triangles.