isosceles triangle
An isosceles triangle is a type of triangle where two sides are equal in length
An isosceles triangle is a type of triangle where two sides are equal in length. This means that two of the angles in the triangle are also equal.
To understand an isosceles triangle better, let’s look at its properties:
1. Two sides of an isosceles triangle are congruent (equal in length).
2. The angles opposite the congruent sides are also congruent.
3. The sum of the angles in an isosceles triangle is always 180 degrees.
Now, let’s solve a problem related to isosceles triangles:
Problem: In an isosceles triangle, the length of the equal sides is 5 cm each, and the angle between them is 72 degrees. Calculate the length of the base.
Solution: Since we know that two sides of an isosceles triangle are equal, we have two equal sides of length 5 cm each. The angle between these sides is given as 72 degrees.
To find the length of the base, we can use the concept of triangle angle sum property. We know that the sum of all the angles in a triangle is 180 degrees.
In an isosceles triangle, let’s denote the length of the base as ‘b’. Since we have the equal sides and the angle between them, we can find the measure of the other two angles. Let’s call one of these angles as ‘x’.
Using the triangle angle sum property, we can write:
72 degrees + 2x + x = 180 degrees
Combining like terms, we get:
3x + 72 = 180
Subtracting 72 from both sides, we have:
3x = 108
Dividing both sides by 3, we get:
x = 36
Now that we have the measure of angle ‘x’, we can find the measure of the third angle, which is also ‘x’ degrees.
To find the length of the base, we can use the sine rule, which states that the ratio of the length of a side to the sine of its opposite angle is constant.
Using the sine rule, we can write:
sin(36 degrees) / 5 cm = sin(base angle) / b
Since the angle opposite the base side is ‘x’ degrees, we substitute the values:
sin(36 degrees) / 5 cm = sin(36 degrees) / b
Cross-multiplying, we get:
b * sin(36 degrees) = 5 cm * sin(36 degrees)
Dividing both sides by sin(36 degrees), we get:
b = 5 cm
So, the length of the base of the isosceles triangle is 5 cm.
I hope this explanation helps you understand isosceles triangles and how to solve problems related to them. If you have any more questions, feel free to ask!
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