Question

Can someone help me please? Thanks!

Answer 1

see below

Explanation:

The property of an isosceles triangle we need to consider is that the height of the triangle is the perpendicular bisector of the base.

so we have two right angled triangles withe the base as `18ft`

(a) when `theta=45^0`

`tan45=y/18`

`color(blue)(y=18xxtan45=18xx1=18ft)`

(b) when `theta=55^0`

`tan55=y/18`

`color(red)(y=18xxtan55=25.71(2dp))`

using a calculator

(c) we want to find the areas in both cases

`A_(Delta)=1/2xx"base "xx"heigt"`

for case (a)

`A_(Deltaa)=1/2xx18xx18`

`color(blue)(A_(Deltaa)=162 ft^2)`

case (b)

`A_(Deltab)=1/2xx18xx25.71`

`color(red)(A_(Deltab)=231.39ft^2(2dp))`