Complicated maths question

An observer at the top of a tower of height 15m sees a man due west of him at an angle of depression 31 (degrees). He sees another man due south at an angle of depression 17 (degrees). Find the distance between the men.

Reply 1

k@tie

10

Fahad

An observer at the top of a tower of height 15m sees a man due west of him at an angle of depression 31 (degrees). He sees another man due south at an angle of depression 17 (degrees). Find the distance between the men.

work out the distance between the ground beneath the tower and the man due west (using tan x = opp/adj)
and the same with the south
then use pythagoreas triangle to get the distance between the 2 men

Reply 2

Fahad

OP

2

i'm having trouble understanding how to draw the diagram :frown:

Reply 3

elpaw

15

first draw a diagram - a right-angled triangle consising of the tower, the ground and a line at 59 degrees from the tower to the ground. work out the hypotenuse of this triangle using trig. this is the distance to W

then another triangle, same as before, but with an angle of 73 degrees, and call this distance S

by pythagoras, the distance is given by d² = S² + W². if you want to draw a diagram, its a right-angled triangle, with the man at the right-angle and the two non-hypotenuse sides of lengths S and W.

of course you could draw all these triangles in one, if you are good at 3d projections.

Reply 4

Fahad

OP

2

the problem is.. i keep on getting 19.26 (3 sf) when the real answer is supposed to be 22.6..

Complicated maths question

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