Thread: Trig

Could do with some help, thanks in advance.

The sloping sides of a factory gable roof make angles of 39o and 52o with the horizontal. The longer sloping side is 75m from top to bottom edge. Find the corresponding length of the shorter side, and the vertical height of the roof, if the walls of the building are 6m high.

Originally Posted by sa87uk

The sloping sides of a factory gable roof make angles of 39o and 52o with the horizontal. The longer sloping side is 75m from top to bottom edge. Find the corresponding length of the shorter side, and the vertical height of the roof, if the walls of the building are 6m high.

first thing you should do is make a sketch. two adjacent right triangles are formed.

from what I can gather from your verbal description ...

height of the gable itself is

length of the shorter side is

vertical height of the roof,

Refer fig below
BE = 6/sin39 (get BE)

AB = AE + EB = 75 + 6/sin39 (Get AB)

AD = AB/sin39 (get AD)


FC = 6/sin52 (get FC)

AC = AD/sin52 Get (AC, AD is calculated aboce)

AF = Ac - FC (Get AF)


Let me know if you still need more clarification.