A local Outdoors club has just hiked to the South Rim of a large Canyon when they spot a climber attempting to scale the taller Northern face. Knowing the distance between the sheer walls of the Northern and Southern faces of the Canyon is approximately 175 m they attempt to compute the distance remaining for the climbers to reach the top of the northern rim. Using a homemade transist they sight an angle of depression of 60 degree to the bottom of the northern face and the angles of elevation of 30 degree and 45 degree to the climbers and the top of the northern rim respectively.
(a) how high is the southern Rim of the Canyon ?
(b) how high is the northern ring ?
(c) how much farther until the climber reaches 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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