How To Draw Dragon Pictures
Trigonometry Functions of Angles.?
There is a giant flaming dragon frozen for all time by a sorceress with a limp on the top of a hill. A modern day angle measuring person sights the top of the dragon, and sees that the angle of elevation is 32 degree. The angle measuring person sights the bottom of the dragon and gets an angle of elevation is 18 degree (the slope of the hill). If the angle measuring person is a “safe” distance of 172ft from the bottom of the frozen dragon, how tall is the dragon>? Round your answer to the nearest foot.
The Law of Sines: Sin A / a = Sin B / b = Sin C / c
The Law of Cosines: a^2 = b^2 + c^2 – 2bc cos A
b^2 = a^2 + c^2 – 2ac cos B
c^2 = a^2 + b^2 – 2ab cos C
Honestly, I have a very hard time to draw a correct picture f this problem. I appropriate it if you’ll show m all the work instead of just one answer.
Thank You
Let
H = height of the frozen dragon
y = distance of the foot of the frozen dragon from the horizontal plane
y = 172*sin 18
y = 53.15 feet
Let
x = distance of the horizontal plane
tan 18 = y/x
and
x = y/tan 18 = 53.15/tan 18
x = 163.58 feet
tan 32 = (H + y)/163.58
tan 32 = (H + 53.15)/163.58
Simplifying the above,
H = 163.58(tan 32) – 53.15
H = 102.22 – 53.15
H = 49 feet (rounded off to the nearest foot)
Hope this helps.
BTW, please check my arithmetic. It can be out of whack at times but the analysis remains the same though.
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