Step-by-step explanation:
well, we have several right-angled triangles here.
the main one from the point in the street to the 2 tops of the poles.
and the 2 side ones of the poles to the point on the street.
we know the angle above the point in the street is 90 degrees, because the other 2 angles of the main triangle are 30 and 60 degrees. and the sum of all angles in a triangle must always be 180 degrees.
as the angles up are 30 and 60 degrees, so are their mirrored twins at the tops of the poles as part of the main triangle.
the Hypotenuse of the main triangle is the connection between the tops of the poles, and is also 80m long.
so, now that we have established the "picture", we can use the law of sine to get all the other side lengths.
a/sin(A) = b/sin(B) = c/sin(C)
where the sides are always opposite of the correlated angles.
so, we know,
80/sin(90) = 80 = a/sin(30) = 2a = b/sin(60)
a = 80/2 = 40m (the connection from the point in the street to the top of the pole under 60°)
b = 80×sin(60) = 69.2820323... m (the connection from the point in the street to the top of the second pole under 30°).
now we use the same principle on the side lengths of the 2 side triangles. their Hypotenuses are the 2 sides we just calculated.
let's start with the one with the round number as Hypotenuse : 40m
40/sin(90) = street distance / sin(30) = 2× street distance
street distance = 40/2 = 20m
that means the street distance of the point in the street to the other pole is 80-20 = 60m
for the pole height(s) we now just use regular Pythagoras
c² = a² + b²
with c being the Hypotenuse.
40² = 20² + pole height²
1600 = 400 + pole height²
1200 = pole height²
pole height = 34.64101615... m
