Alyosha and ivan are standing between two buildings they know to be equal height. the buildings are 500 feet apart. looking up at the westernmost building, they form a 30 degree angle. looking to the easternmost building, they form a 45 degree angle. how far away from each building are they?
+128731 Call the distance to the westernmost building = x ......and call the height of both buildings = h
So we have, with the respect to the westernmost building.....
tan 30 = h/x solving for h, we have ...... h = x * tan 30
And with respect to the easternmost building, we have
tan 45 = h/(500 - x) = x *tan(30)/ (500 - x) simplify
tan 45/ tan 30 = x / (500 - x)
1/ [1/ √3] = x/ (500 - x)
√3 = x / (500 - x)
√3(500 - x) = x
√3*500 = x(1 +√3)
x = (√3)500/(1 +√3) = about 317 ft ....and this is the distance to the westernmost building
And the distance to the easternmost building is (500- x) ft = (500 - 317)ft = about 183 ft
+128731 Call the distance to the westernmost building = x ......and call the height of both buildings = h
So we have, with the respect to the westernmost building.....
tan 30 = h/x solving for h, we have ...... h = x * tan 30
And with respect to the easternmost building, we have
tan 45 = h/(500 - x) = x *tan(30)/ (500 - x) simplify
tan 45/ tan 30 = x / (500 - x)
1/ [1/ √3] = x/ (500 - x)
√3 = x / (500 - x)
√3(500 - x) = x
√3*500 = x(1 +√3)
x = (√3)500/(1 +√3) = about 317 ft ....and this is the distance to the westernmost building
And the distance to the easternmost building is (500- x) ft = (500 - 317)ft = about 183 ft
