To find the height of a right triangle, you can use the relationship between the triangle’s area and its base and height. The area of a right triangle is calculated using the formula:
A = (1/2) × base × height
In a right triangle, you can choose one of the two shorter sides as the base. Let’s denote the base as ‘b’ and the height as ‘h’. Rearranging the formula to find the height gives us:
h = (2 × A) / b
If you already know the area of the triangle and the length of the base, you can simply plug those values into the equation to find the height.
For example, if a right triangle has an area of 30 square units and you choose one leg (base) to be 5 units, the height would be:
h = (2 × 30) / 5 = 12 units
This method works perfectly, as it allows you to find the height based on the area and a known base. If you do not know the area, but you have the lengths of both legs, you can find the area first, as the area of a right triangle is also half the product of the two legs:
A = (1/2) × leg1 × leg2
By identifying the legs and calculating the area, you can then use it to find the height as described earlier.