A local Outdoors Club has just hiked to the south rim of a large canyon, when they spot a climber attempting to se
climber attempting to scale the talle
northern face. Knowing the distance between the shear walls of the northern and southern faces of the canyon is an
n faces of the canyon is approximately
175m, they attempt to compute the distance remaining for the climbers to reach the top of the northern rim. Usinen
northern rim. Using a homemade
transit, they sight an angle of depression of 60° to the bottom of the north face, and angles of elevation of 30° and 45° to
climbers and top of the northern rim respectively.
(a) How high is the southern rim of the canyon?
(b) How high is the northern rim?
(c) How much farther until the climber reached the top?
Answers
Height of southern Rim = 175 / √3 m , Northern rim Height = 350 / √3 m , 175 (√3 - 1)/√3 m is to be farther climbed
Step-by-step explanation:
Tan 60 = 175 / Height of southern Rim
=> √3 = 175 / Height of southern Rim
=> Height of southern Rim = 175 / √3 m
Tan 30 = ( Northern rim Height - southern Rim height)/175
=> 1/√3 = ( Northern rim Height - 175 / √3)/175
=> 175 / √3 = Northern rim Height - 175 / √3
=> Northern rim Height = 350 / √3 m
Tan 45 = ( Northern rim Height - southern Rim height + further distance)/ 175
=> 1 = (175 / √3 + Further Distance)/175
=> Further Distance = 175 - 175 / √3
=> Further Distance = 175 (√3 - 1)/√3 m
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Answer:
Step-by-step explanation:
Tân 60 = 175 / Chiều cao của vành đai phía Nam
=> 3 = 175 / Chiều cao của vành đai phía nam
=> Chiều cao của vành đai phía Nam = 175/3 m
Tân 30 = (Chiều cao vành phía Bắc - Chiều cao vành phía Nam) / 175
=> 1/3 = (Chiều cao vành phía Bắc - 175/3) / 175
=> 175/3 = Chiều cao vành phía Bắc - 175/3
=> Chiều cao vành phía bắc = 350/3 m
Tân 45 = (Chiều cao vành phía Bắc - Chiều cao vành phía Nam + khoảng cách xa hơn) / 175
=> 1 = (175 / √3 + Khoảng cách xa hơn) / 175
=> Khoảng cách xa hơn = 175 - 175/3
=> Khoảng cách xa hơn = 175 (3 - 1) / 3 m