Suppose you have an isosceles triangle, and each of the equal sides has a length of r feet. Suppose the angle formed by those two sides is t. Then the area of the triangle is?
To find the area of an isosceles triangle, you can use the formula:
Area = (1/2) * base * height
However, in this case, we haven't been given the base and height of the triangle directly. Instead, we have the equal sides (length r) and the angle formed by those sides (angle t).
To find the base and height, we can use trigonometry and geometry.
First, let's draw the triangle:
```
A
/ \
/ \
c/_______\c
B a B
```
In this diagram, the equal sides are labeled as "a" and the base as "c" (since the height will be perpendicular to the base).
To find the base (c) and height, we can use the sine function:
sin(t) = opposite/hypotenuse
In this case, the opposite side is the height (h) and the hypotenuse is the equal side (a).
sin(t) = h/a
Rearranging the formula to solve for h:
h = a * sin(t)
Given that the equal sides have a length of r, the base (c) is equal to 2r (since it's made up of two equal sides). So,
h = 2r * sin(t)
Now that we have the base (c) and height (h), we can substitute them into the formula for finding the area of a triangle:
Area = (1/2) * base * height
Substituting the values:
Area = (1/2) * 2r * sin(t)
= r * sin(t)
Therefore, the area of the isosceles triangle is r * sin(t).