Question

!50 POINTS! (2 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW

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Answer 1

1) 243

2) x = 190.9

z = 190.9

y = 260.4

Explanation:

`tan(\theta) =(opp)/(adj)\\\\\implies tan(45) =(h)/(x)\\\\\implies h = x\;tan(45)\\\\= 243*1\\\\= 243`

2)

`tan(\theta) =(opp)/(adj)\\\\\implies tan(45) =(x)/(z)\\\\\imlplies z\;tan(45) = x\\\\\implies z = x`

`sin(\theta) =(opp)/(hyp)\\\\\implies sin(45) =(x)/(270)\\\\\imlplies 270\;sin(45) = x\\\\\implies (270)/(√(2) ) = x\\\\\implies x = 190.9\\\\\implies z = 190.9`

Let the side opposite to 20° be 'p'

`tan(\theta) =(opp)/(adj)\\\\\implies tan(20) =(p)/(z)\\\\\imlplies z\;tan(20) = p`

y = p + x

= z tan(20) + x

= x tan(20) + x

= x * [tan(20) + 1]

`= (270 (tan(20) + 1))/(√(2) )`

=260.4