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A geologist measured a 40-degree angle of elevation to the top of a mountain. After moving 0.5m farther away, the angle of elevation was 34 degrees. How high is the top of the mountain?
this can be solve by functions of a right triangle the tan(theta) which is equal to opposite side/ adjacent side which the opposite side is the height that we looking for. and the adjacent side is the distance from his feet to the bottom of the mountain
let h the height of the mountain and d is the distance of the person from the mountain from the first measurement
at first situation measurement tan (40) = h/d and make d in terms of h by algebra skills d = h/tan (40)
at the second situation he move 0.5m farther so it will plus to the distance at the first situation then it becomes tan (34) = h/d +0.5 then manipulate the equation you have the value of d at the first situation so just substitute the d then it becomes tan (34) = h / (h/tan40) + 0.5 then solve the h by your algebraic skills tan34 (h/tan40 + 0.5) =h distribute the tan(34) h tan34/tan40 + (0.5)tan34 = h combine like terms 0.5(tan34) = h (1 - tan34/tan40 ) then you get the h h = 0.5(tan34)/(1 - tan34/tan40 )
h = 1.719 m and tell your teacher that it is not mountain it is punso haha joke..
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