An isosceles triangle is a triangle with two sides that are the same length. Find the measure of the two equal angles to the nearest degree in a triangle that has sides of length 5ft., 5ft., and 6ft.
In your isosceles triangle create a right-angled triangle with a base of 3 and hypotenuse of 5
then cos(theta) = 3/5
theta = 53.13ยบ
To find the measure of the two equal angles in an isosceles triangle, we can use the concept of the Isosceles Triangle Theorem.
The Isosceles Triangle Theorem states that in an isosceles triangle, the two angles opposite the equal sides are congruent (have the same measure).
In the given triangle with sides of length 5ft, 5ft, and 6ft, we can identify the two equal sides (both sides with a length of 5ft).
Since the sum of the interior angles in a triangle is always 180 degrees, we can use this information to find the measure of the third angle.
Let's denote the two equal angles as "x" degrees. According to the Isosceles Triangle Theorem, these two angles are congruent.
The three angles in the triangle can be labeled as follows:
Angle A = x degrees (vertex angle)
Angle B = x degrees (base angle)
Angle C = ? degrees (third angle)
Now, let's use the fact that the sum of the interior angles in a triangle is 180 degrees:
Angle A + Angle B + Angle C = 180 degrees
Substituting the values, we have:
x + x + Angle C = 180
Combining like terms, we get:
2x + Angle C = 180
Next, let's substitute the given value for the length of the third side:
x + x + 6 = 180
Simplifying:
2x = 174
Dividing both sides by 2, we find:
x = 87
Therefore, each of the equal angles in the triangle measures approximately 87 degrees to the nearest degree.