An isosceles triangle has a base 36 cm long and a base of 65 degrees. Find its perimeter.
I'm not sure if this is right but my answer is 1250.4 in^2
To find the perimeter of the isosceles triangle, we need to determine the lengths of the two equal sides.
Given that the base of the triangle is 36 cm long and the base angle is 65 degrees, we can use the properties of isosceles triangles to find the lengths of the other sides.
In an isosceles triangle, the base angles are equal, so we have two angles of 65 degrees each. The sum of the interior angles of a triangle is always 180 degrees, so we can find the third angle by subtracting twice 65 degrees from 180 degrees: 180 - 2*65 = 50 degrees.
Since we now have the measure of all three angles, we can use the Law of Sines to find the side lengths. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.
Let's call the equal side length x. The Law of Sines can be written as:
x / sin(65 degrees) = 36 cm / sin(50 degrees)
Simplifying this equation, we have:
x = (36 cm * sin(65 degrees)) / sin(50 degrees)
Using a calculator, we find that x ≈ 42.176 cm.
Now that we know the lengths of the two equal sides (approximately 42.176 cm each), we can calculate the perimeter by adding the lengths of all three sides:
Perimeter = 36 cm + 42.176 cm + 42.176 cm ≈ 120.352 cm
So, the approximate perimeter of the isosceles triangle is 120.352 cm.