Answer:
The drawing in the attached figure
see the explanation
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
In this problem
we have an isosceles triangle (because has two equal interior angles)
see the attached figure to better understand the problem
step 1
Find the length side AB
In the right triangle ABD
[tex]cos(40^o)=\frac{BD}{AB}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
we have
[tex]BD=BC/2=5/2=2.5\ in[/tex] ---> because is an isosceles triangle (the height bisect the base)
substitute
[tex]cos(40^o)=\frac{2.5}{AB}[/tex]
[tex]AB=\frac{2.5}{cos(40^o)}=3.3\ in[/tex]
Find the length side AC
we know that
AC=AB ----> by definition of isosceles triangle
so
[tex]AB=3.3\ in[/tex]
step 2
Find the perimeter
[tex]P=AB+BC+AC[/tex]
[tex]P=3.3+5+3.3=11.6\ in[/tex]
step 3
Find the height AD
In the right triangle ABD
[tex]tan(40^o)=\frac{AD}{BD}[/tex] ----> by TOA (opposite side divided by the adjacent side)
[tex]AD=tan(40^o)BD[/tex]
substitute the given values
[tex]AD=tan(40^o)(2.5)=2.1\ in[/tex]
Find the area of triangle
[tex]A=\frac{1}{2}(BC)(AD)[/tex]
substitute
[tex]A=\frac{1}{2}(5)(2.1)=5.25\ in^2[/tex]
Answer: It makes one unique triangle
Step-by-step explanation:
