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Answer:
Properties of isosceles triangle:
- Two sides are congruent(i.,e equal)
- Corresponding angles opposite to these sides are equal.
- A Perpendicular drawn to the third side from the corresponding vertex will bisect the third side.
- Also the altitude drawn will divide the isosceles triangle into two congruent right triangles.
As per the given statement:
Congruent sides(a) = 3 feet And Vertex angle() =
Let the length of the base(QR) of an isosceles triangle PQR be 2b.
By isosceles properties, in triangle PQR , the median of an isosceles triangle from its vertex angle is also the perpendicular bisector of the base.
Also, this line divides the triangle into two congruent right angled triangles whose hypotenuse is 3 feet,
and
In a right angle triangle QSP
Using sine ratio formula;
Hypotenuse sides = PQ = 3 ft and Opposite side = QS = b ft
Solve for b using using sine ratio:
or
Simplify:
b = 0.902117398
Length of the base of an isosceles triangle PQR = 2b = 2(0.902117398) = 1.8042348
Therefore, the approximate length of the base of an isosceles triangle is, 1.8 feet
