It is given that a banner shaped like a right triangle has a hypotenuse of 26 feet and a leg of 10 feet. We will find the area of the banner.
We will first identify what we need to find the area of a triangle. Let's remember that the area of a triangle is half the product of the base b and the height h. Therefore, to find the area of a triangle, we need the length of a base and its corresponding height.
A=1/2bh
Notice that in our right triangle, when we consider the given leg of 10 feet as a base, the other leg is the corresponding height h.
Therefore, in order to calculate the area of our triangle, we need to find the length of the other leg h. Since the right triangle has a hypotenuse of 26 feet and a leg of 10 feet, we can use the Pythagorean Theorem to find the value of h.
a^2+b^2=c^2 ⇔ 10^2+ h^2= 26^2
Let's solve this equation for h.
The length of the other leg is 24 feet. Now, we have all the information needed to find the area of the banner. Let's substitute b= 10 and h= 24 into the area formula, and calculate it.
