Question

What is the length of the base? help me please thank u ;)​

Answer 1

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units$

____________________________________

$\large \tt Solution \: :$

As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.

$\textsf{let each of those angles measure ' x ' }$

$\qquad \tt \rightarrow \:x + x + 60 = 180$

[ sum of all interior angles of a triangle ]

$\qquad \tt \rightarrow \:2x + 60 = 180$

$\qquad \tt \rightarrow \:2x = 180 - 60$

$\qquad \tt \rightarrow \:2x = 120$

$\qquad \tt \rightarrow \:x = \cfrac{120}{2}$

$\qquad \tt \rightarrow \:x = 60 \degree$

Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.

henceforth, all its sides are equal to one another.

$\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units$

Answer 2

Answer:   26

=============================================================

Explanation:

a = 26 and b = 26 are the congruent legs

angle C = 60 degrees is between sides 'a' and b

c = unknown base which is opposite angle C

We'll use the law of cosines to find this missing side.

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 26^2 + 26^2 - 2*26*26*cos(60)

c^2 = 676

c = sqrt(676)

c = 26

It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.

---------------

Here's another way to see why we have an equilateral triangle.

The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180

x+x+60 = 180

2x+60 = 180

2x = 180-60

2x = 120

x = 120/2

x = 60

Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.

If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.