ACT Math : How to find the height of a right triangle
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Example Questions
Example Question #21 : Right Triangles
Given a right triangle with a leg length of 
1. Use the pythagorean theorem with 
2. Solve for 
(Notice that this right triangle is also a 
Example Question #21 : Triangles
A 
To answer this, we first need to understand that we are trying to find the leg of a right triangle. The ladder, when leaned against the wall, forms a right triangle where the ladder is the hypotenuse, the wall is one leg, and the ground between the ladder and the wall is the other leg.
To find how high up the ladder touches the wall, we use the Pythagorean Theorem, which is:
We then rearrange to solve for one of the legs by subtracting 
We can now plug in our values of 10 for the hypotenuse and one of our legs (in this case, 
We can then take the square root of this equation to get an answer for
The question asked us to approximate, so we must round to the nearest whole number. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:
Therefore, our answer is 
Example Question #23 : Right Triangles
Right triangle 
The formula for the area of a triangle is 
Example Question #24 : Right Triangles
Find the height of a right triangle given a base of 
To solve, simply realize this is one of our special right triangles, 
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