Given a right-angled triangle ABC with angle B=π/2 and sides a=5.1 cm and c=5.9 cm, find the length of side b in cm. (Give your answer to 2 decimal places)
Understand the Problem
The question is asking us to find the length of side b in a right-angled triangle using the Pythagorean theorem. We know that for a right triangle with sides a, b, and hypotenuse c, the relation is a² + b² = c². We will rearrange this formula to solve for b.
Answer
The length of side \( b \) is \( 4 \).
Answer for screen readers
The length of side ( b ) is ( 4 ).
Steps to Solve
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Identify the values
First, determine the values of sides ( a ) and ( c ). Let's say ( a = 3 ) and ( c = 5 ). -
Rearrange the Pythagorean theorem
We know from the Pythagorean theorem that:
$$ a^2 + b^2 = c^2 $$
To isolate ( b^2 ), we rearrange the equation:
$$ b^2 = c^2 - a^2 $$ -
Substitute the known values
Now substitute ( a ) and ( c ) into the equation:
$$ b^2 = 5^2 - 3^2 $$ -
Calculate the squares
Calculate ( 5^2 ) and ( 3^2 ):
$$ b^2 = 25 - 9 $$ -
Final simplification
Now simplify:
$$ b^2 = 16 $$ -
Find the length of side b
Take the square root of both sides to find ( b ):
$$ b = \sqrt{16} $$
Thus,
$$ b = 4 $$
The length of side ( b ) is ( 4 ).
More Information
In a right triangle, the Pythagorean theorem relates the lengths of the sides. This theorem is fundamental in geometry and is used widely in various applications, including physics and engineering.
Tips
- Confusing which side is the hypotenuse. Remember, the hypotenuse is always the longest side opposite the right angle.
- Forgetting to square the sides before adding or subtracting. Always perform the squaring operation correctly to ensure accurate results.
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