URGENT! TRIGO APPLICATIONS FOR E MATHS!

bonkysleuth SG

A and B are 2 houses, 40 m apart, on the same horizontal line as the foot F of a building TF. The angles of depression of A and B from top of building are 25 deg and 58 deg respectively. Find the possible heights of the building.

answer's are 26.3m and 14.4 m. I can't get 14.4m...

Please do reply swiftly if possible because i'm having my exam tomorrow. thanks.

FireIce SG

A and B can be one on each side of the building
or both on the same side

as in

A----- F---------B
or
F ----B-----A

(smaller angle of depression = further away)

u need to have 2 diagrams

maurizio13 SG

A and B can be one on each side of the building
or both on the same side

as in

A----- F---------B
or
F ----B-----A

(smaller angle of depression = further away)

u need to have 2 diagrams

老师？？

eagle SG

There are two different ways for the houses to be placed

Taking the difference of the ground distance,
h / tan 25° - h / tan 58° = 40
h (1 / tan 25° - 1 / tan 58°) = 40
1.5196 h = 40
h = 26.3 m

Taking the summation of the ground distance,
h / tan 25° + h / tan 58° = 40
h (1 / tan 25° + 1 / tan 58°) = 40
2.769 h = 40
h = 14.4 m

Answer placed on ExamWorld as well. Thanks for the contribution :D

Regards,
Eagle