Answer:
A. 1.8 ft.
Step-by-step explanation:
Let x be the measure of each base angle.
We have been given that in an isosceles triangle the congruent sides are 3 feet and the vertex angle is 35°. We are asked to find the length of base of isosceles triangle.
Using angle sum property of triangle we can set an equation to find the value of x as:
[tex]x+x+35^{\circ}=180^{\circ}[/tex]
[tex]2x+35^{\circ}=180^{\circ}[/tex]
[tex]2x+35^{\circ}-35^{\circ}=180^{\circ}-35^{\circ}[/tex]
[tex]2x=145^{\circ}[/tex]
[tex]\frac{2x}{2}=\frac{145^{\circ}}{2}[/tex]
[tex]x=72.5^{\circ}[/tex]
Since the vertex angle of an isosceles triangle is the included angle of both congruent sides, so we will use law of sines to solve for the length of base of our given triangle.
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex], where, a, b and c are the opposite sides to angles A, B and C respectively.
Upon substituting our given values in above equation we will get,
[tex]\frac{a}{sin(35^{\circ})}=\frac{3}{sin(72.5^{\circ})}[/tex]
[tex]\frac{a}{0.573576436351}=\frac{3}{0.953716950748}[/tex]
[tex]a=\frac{3}{0.953716950748}\times 0.573576436351[/tex]
[tex]a=3.1455873754\times 0.573576436351[/tex]
[tex]a=1.804234797\approx 1.8[/tex]
Therefore, the length of the base of our given isosceles triangle is 1.8 ft and option A is the correct choice.
