Question

Find the values of x,y,w, and v in the figure below

Answer 1

x=8.45cm

`\angle \ y=57.67\textdegree`

w=18.13cm

v=5.35cm

Explanation:

#Use Sine Rule to calculate x and w:

`\ Sine \ Rule:\\(a)/(sin A)=(b)/(sin B)=(c)/(sin C)\\\\(20)/(sin 90\trxtdegree)=(x)/(sin 25\textdegree)\\\\x=8.45cm\\\\(20)/(sin 90\textdegree)=(w)/(sin 65\textdegree)\\\\w=18.13cm`

Hence x=8.45cm and w=18.13cm

#Further using Sine Rule to calculate y and v:

`\ Sine \ Rule:\\(a)/(sin A)=(b)/(sin B)=(c)/(sin C)\\\\(10)/(sin 90\trxtdegree)=(8.45)/(sin y\textdegree)\\\\y=57.67\textdegree\\\\(10)/(sin 90\textdegree)=(v)/(sin (90-57.67)\textdegree)\\\\v=5.35cm`

Hence v=5.35cm and
`\angle \ y=57.67\textdegree`