Question

What is the approximate length of the base of an isosceles triangle if the congruent sides are 3 feet and the vertex angle is 35°? impossible to tell 1.8 ft 2.8 ft 3.2 ft

Answer 1

A. 1.8 ft.

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:

`x+x+35^(\circ)=180^(\circ)`

`2x+35^(\circ)=180^(\circ)`

`2x+35^(\circ)-35^(\circ)=180^(\circ)-35^(\circ)`

`2x=145^(\circ)`

`(2x)/(2)=(145^(\circ))/(2)`

`x=72.5^(\circ)`

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.

`(a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C))`, 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,

`(a)/(sin(35^(\circ)))=(3)/(sin(72.5^(\circ)))`

`(a)/(0.573576436351)=(3)/(0.953716950748)`

`a=(3)/(0.953716950748)* 0.573576436351`

`a=3.1455873754* 0.573576436351`

`a=1.804234797\approx 1.8`

Therefore, the length of the base of our given isosceles triangle is 1.8 ft and option A is the correct choice.

Answer 2

`1.80\ ft`

Explanation:

we know that

An isosceles triangle has two equal sides and two equal angles.

The third angle is called the vertex angle

Remember that

the sum of the internal angles in the triangle is equal to
`180\°`

Find the measure of the base angles

Let

x------> the measure of the base angle

`2x+35\°=180\°`

`2x=180\°-35\°`

`x=72.5\°`

Find the length of the base

Applying the law of sines

Let

b------> the length of the base

`(b)/(sin(35\°))=(3)/(sin(72.5\°)) \\\\b=3*sin(35\°)/sin(72.5\°)\\ \\b=1.80\ ft`