What would the angles need to be increased to ?

Question

An isosceles triangle has two angles of 25°. The length of the side joining these two angles is 48mm. What would the angles need to be increased to in order to double the area of the triangle if the 48mm side remains unchanged

Answer 1

desmos.com/calculator/q6idyzrwxe

Answer 2

α=25°

β=25°

γ=130°

c=48mm

area=base*h/2

To make this into 2 right triangles: α=25°

β=65°

γ=90°

b=24mm

We need side "a"; so; a/sinα=b/sinβ=c/sinγ.

a/.4226=24/.9063=26.481; a=11.191

ab=268.593; area of the original triangle.

If the angles are changed; the sides are also.

New area=537.186=base*h/2

Now 24mm is side "a".

So 24*b=1074.373sq/mm

b=44.766mm

a=24; b=44.766; c=a^2+b^2=c^2

=50.793mm

c/sinγ=50.793 (sin 90°=1);=44.766/sinβ; sinβ=.881; β=61.8°; α=28.2°.

For the isoc; β=123.6°.

Answer 3

Use right triangle tan relationship increasing the angles. I doubled the height to double the area.

Area of a triangle = base • height divide by 2

I found the height of the original triangle to be 11.2. So when I doubled it I had a new height of 22.4.

Using inverse Tan (22.4/24) I came up with a

43.025 degree angle. Hope it makes sense.