Krishna
0

Step 1: Use the area formula of the isosceles triangle to calculate base.

When Two equal sides are a, a & included angles

Area of an isosceles triangle A = \frac{1}{2}* a^2 *\sin \theta

s is the length of one of the two equal sides.

θ is the angle between the two equal sides.

Step 2: Find the angle between the two equal sides (\theta).

EXAMPLE: \sin \theta = \frac{2 * A}{a^2}    (Rewrite the area formula of the isosceles triangle)

\sin {\theta} = \frac{2 * 6}{5^2}

\sin {\theta} = \frac{12}{25}

\theta = arcsin ({\frac{12}{25}})   .................(1)

Use the trigonometry calculate to find this value

Step 3: Divide the isosceles triangle into two right angle triangles

Step 4: Set up a formula by using the right angle triangle ratios to find the base

NOTE: \sin (\frac{α}{2}) = \frac{\frac{b}{2}}{a}

Step 5: Substitute the known values in the formula

EXAMPLE: \sin(\frac{\theta}{2}) = \frac{b}{2a}

b = 2 a \sin(\frac{\theta}{2})

b = 2 * 5 \sin(\frac{\arcsin ({\frac{12}{25}})}{2})     (Since Substitute \theta value

b\ =\ 10\ \cdot\sin\left(\frac{1}{2}\cdot\arcsin\left(\frac{12}{25}\right)\right)

Use the trigonometry calculate to find this value

b = 2.48