10) A skier at the Murky Mountain ski resort is on top of a slope that is a mile
ID: 2904670 • Letter: 1
Question
10) A skier at the Murky Mountain ski resort is on top of a slope that is a mile and a quarter directly east of the lodge. The angle of depression from the skier to the roof of the lodge is 9degree. Notes: 1 mile = 5280 feet. Answer in feet to the nearest tenth of a foot. a) How much higher is the skier compared to the roof of the lodge? b) What is the direct line radio distance from the skier to the lodge? 11) The height of a flag waving on the top of a flag pole is estimated this way: I measure off a distance of 200 ft from the base of the flag pole, and then measure the angle of elevation of the top of the flag, finding it to be 32degree. The angle of elevation from the same reference point to the base of the flag is 29.5degree. Find the height of the flag.Explanation / Answer
angle of depression =90
slope =1mile and quarter
1mile=5280feet
1/4mile=1320feet
total slope distance=1320+5280
=6600
apply trigonometry
cos 90=base/hypotenuse
cos 90=height of skier with repect to roof of lodge/slope
-0.9111=h/6600
h=- 0.911*6600
h= - 6013.459
but distance cannot be negative so h=6013.459 feet
b) horizontal distance calculated as
sin 90=perpendicular/hypotenuse
0.4121=distance(horizontal)/6620
horizontal distance=6620*0.4121
horizontal distance=2728.102 feet
ANSWER OF 11 QUESTION AS FOLLOWS
angle of elevation to top of flag =320
angle of elevation to bottom of flag = 29.50
then distance=200 feet (given)
tan 320=perpendicular/base
=height from ground to top of flag/200
0.661 =H/200
H=0.661*200
H=132.2 feet (it is the distance from ground to top of flag)
tan29.50=height from ground to bottom of flag/200
2.781*200=h
h=556.297
Height of flag=556.297-132.2
Height of flag=424.097 feet
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