Video Transcript
In the displayed model of a house,
what angle does the roof make with the horizontal, given that triangle 𝐴𝐸𝐵 is
isosceles?
It’s probably most useful to begin
this question by highlighting the triangle 𝐴𝐸𝐵 that we want to consider. This triangle forms the roof of
this house, and we’re told that it’s isosceles. We should recall that in an
isosceles triangle, we have two sides equal in length and two base angles are
equal. So in this diagram, the side 𝐴𝐸
is equal to the side 𝐴𝐵 and the angle 𝐴𝐸𝐵 is equal to the angle 𝐴𝐵𝐸.
Now that we’ve had a look at the
diagram, let’s focus on what we’re asked, to find the angle that the roof makes with
the horizontal. That means that we’re really
looking for the angle created by the slope of the roof and the horizontal axis. Either of the two base angles would
give us the answer for this. So let’s see if we can work out one
of these angles, angle 𝐴𝐵𝐸.
In order to do this, we’ll need to
remember an important fact about the angles in a triangle. And that is that the angles in a
triangle add up to 180 degrees. This means that we can write that
angle 𝐵𝐴𝐸 plus angle 𝐴𝐸𝐵 plus angle 𝐴𝐵𝐸 is equal to 180 degrees. We’re given that angle 𝐵𝐴𝐸 is
107 degrees. So if we subtract 107 degrees from
both sides of this equation, we get that angle 𝐴𝐸𝐵 plus angle 𝐴𝐵𝐸 is equal to
73 degrees. As we have an isosceles triangle,
we know that our two base angles are equal. So angle 𝐴𝐸𝐵 is equal to angle
𝐴𝐵𝐸.
We could think of this then that
two times angle 𝐴𝐵𝐸 is 73 degrees. And so to find angle 𝐴𝐵𝐸, we
must divide both sides of this equation by two, which means that the measure of
angle 𝐴𝐵𝐸 is 36.5 degrees as a decimal. We can therefore give our answer
that the angle that the roof makes with the horizontal is 36.5 degrees.
