From a point on the ground, the angle of elevation to the top of a mountain is 31 degrees. Moving out a distance of 200 m(on a level plane( to another point on the ground, the angle of elevation is 18 degrees. Find the height of the mountain
How do I solve this one? Im not sure what im doing wrong here. heres how i tried it
a=height of mountain
x=length of triangle base from highest point of mountain to 31degree angle end
So we have the two base angles and the length of the entire base, so the way i tried solving this was by trying to flush out the length of the base from the 18 degree angle, to the point where the peak meets the base, then solving for X after that... Here goes....
(200-x)tan31=xtan18
200tan31=xtan31+xtan18
x(tan31+tan18)=200tan31
x=(200tan31)/(tan31+tan18)
x=129.806
so from here i should have the base length of the triangle from the peak point to the end of the 18 degree angle... so I now have the required side length and angle to solve for A (so i think)
so i'm left with:
129.806Tan(18)=45.24
at this point my brain explodes, im sure its something stupid i'm doing wrong, or im overthinking it. any help would be great
How do I solve this one? Im not sure what im doing wrong here. heres how i tried it
a=height of mountain
x=length of triangle base from highest point of mountain to 31degree angle end
So we have the two base angles and the length of the entire base, so the way i tried solving this was by trying to flush out the length of the base from the 18 degree angle, to the point where the peak meets the base, then solving for X after that... Here goes....
(200-x)tan31=xtan18
200tan31=xtan31+xtan18
x(tan31+tan18)=200tan31
x=(200tan31)/(tan31+tan18)
x=129.806
so from here i should have the base length of the triangle from the peak point to the end of the 18 degree angle... so I now have the required side length and angle to solve for A (so i think)
so i'm left with:
129.806Tan(18)=45.24
at this point my brain explodes, im sure its something stupid i'm doing wrong, or im overthinking it. any help would be great
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Height of the mountain = h m
Distance from the foot of the mountain in the 1st position = x m
hence, h/x = tan 31deg = 0.600 ........ (1)
Distance from the foot of the mountain in the 2nd position = x + 200 m
hence, h / (x + 200) = tan 18deg = 0.325 ........ (2)
Dividing (1) by (2), we get (x + 200) / x = 0.600 / 0.325 = 1.85
=> 1 + (200/x) = 1.85, => 200/x = 0.85, => x = 200/(0.85)
Substituting the value of x in (1) we get h = {200*(0.600)} / (0.85) = 141.18 m
Distance from the foot of the mountain in the 1st position = x m
hence, h/x = tan 31deg = 0.600 ........ (1)
Distance from the foot of the mountain in the 2nd position = x + 200 m
hence, h / (x + 200) = tan 18deg = 0.325 ........ (2)
Dividing (1) by (2), we get (x + 200) / x = 0.600 / 0.325 = 1.85
=> 1 + (200/x) = 1.85, => 200/x = 0.85, => x = 200/(0.85)
Substituting the value of x in (1) we get h = {200*(0.600)} / (0.85) = 141.18 m