Question

from the top of an 800 foot tall car talk tower, tom sees a plane; the angle of elevation is 67 degrees. at the same instant tay who is on the ground one mile from the building notes that his angle of elevation to the plane is 81 degrees and that his angle of elevation to the top of the tower is 8.6. assuming that tom and ray and the airplane are in a plane perpendicular to the ground, how high is the airplane

Answer 1

Answer: 25971.7 meters

Answer 2

Height of plane = 25971.7 meters

Explanation:

let H =height of plane

Let x = distance ray to the point under the plane

800 foot = 245meters

1 mile = 1609meters.

Tan 81 =
`(H)/(1609+x)` -----------------------(1)

Tan 67 =
`(H-245)/(x)` -----------------------(2)

6.3134 =
`(H)/(1609+x)` ------------------------(3)

2.3556 =
`(H-245)/(x)` -----------------------(4)

from (3) and (4)

H = 10158.26 + 6.3134x ---------------(a)

H = 245 + 2.2336x ---------------(b)

equating both (a) and (b) we have:

9913.26 = 3.9576x

x = 2504.74

Subst. x = 2504.74 into (a)

H = 25971.7meters