Shortcut -Heights and Distances
Solution using tan Ɵ .
Question:
Jack Sparrow from a boat saw a lighthouse of height 100m at an angle of elevation, 60o. What is the distance between Jack Sparrow and the tower?
Answer: tan Ɵ =opposite side/adjacent side
tan 60 =$\dfrac{100}{x}$= √3=$\dfrac{100}{x}$= x = 57.7 m
Shortcut -Heights and Distances
Solution using Pythagoras theorem:
$Hypotenuse^{2}=Opposite^{2}+Adjacent^{2}$
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?
Answer: $hyp^{2}$ = $opp^{2} + adj^{2}$
$500^{2}$= $400^{2} + x^{2}$
$x^{2}$= 90000
x = 300 m