# Shortcut of Heights and Distances

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Shortcut 85:
Using tanƟ
Ɵ                                tan

0                                    0

30                            $1/\sqrt3$

45                                  1

60                             $\sqrt3$

90                              $\infty$
Question:
A man on a boat saw a tower of height 100m at an angle of 60o. What is the distance between the man and the tower?

tan 60 = 100/x
√3 = 100/x
x= 100/√3

Shortcut 86:
Using Pythagoras theorem
$hyp^2=opp^2+adj^2$
Question:
A man looks at the top of a tower which is 400m height. The minimum distance between him and top of the tower is 500m. What is the distance between him and the base of the tower?