On a isosceles triangle, how would you find the area and perimeter when given the bases: 12 and 32 and a 45 degree angle?
You seem to have conflicting data.
Where is the 45° angle ?
if the base is 12 and the two equal sides are 32 each, then there can't be a 45° angle.
If the base is 32 and the two equal sides are 12, you will not be able to draw the triangle, since that is not possible.
In the bottom left hand corner. The sides are blank. I'm just confuses on how to find the sides & finding the perimeter & area
Still makes no sense.
If the bottom angle is 45° and it is isosceles, then you have a right-angled triangle.
To find the area and perimeter of an isosceles triangle with given bases and a 45-degree angle, you can follow these steps:
1. Determine the length of the equal sides:
Since the triangle is isosceles, we know that the two equal sides are the same length. To find their length, you can use the law of cosines:
Let's denote the equal side length as "a".
Using the formula: a^2 = b^2 + c^2 - 2bc * cos(A), where A is the angle opposite to side "a":
a^2 = 12^2 + 32^2 - 2 * 12 * 32 * cos(45°)
a^2 = 144 + 1024 - 768√2
a^2 = 1168 - 768√2
Taking the square root of both sides, we find the length of the equal sides: a ≈ √(1168 - 768√2)
2. Calculate the area:
Since we have the base and height of the triangle, we can use the formula for the area of a triangle: A = 0.5 * base * height.
The base of the triangle is one of the given bases, so we can use 12 or 32 (let's choose 12).
The height can be found using trigonometry: height = a * sin(A).
Plugging the values, we get:
A ≈ 0.5 * 12 * (√(1168 - 768√2)) * sin(45°)
3. Calculate the perimeter:
Since we already know the lengths of the equal sides, we can calculate the perimeter by summing all the sides.
Perimeter = 2 * equal side + base
Perimeter = 2 * √(1168 - 768√2) + 12
By following these steps, you can find the area and perimeter of an isosceles triangle given its bases and a 45-degree angle.