To find the length of the other side of a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The formula for the Pythagorean theorem is:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In this problem, we know:
- \( c = 8.5 \) meters (hypotenuse)
- \( a = 4 \) meters (one of the sides)
We need to find \( b \) (the other side).
First, we square the known side and the hypotenuse:
\[ c^2 = 8.5^2 = 72.25 \]
\[ a^2 = 4^2 = 16 \]
Next, we use the Pythagorean theorem and solve for \( b^2 \):
\[ c^2 = a^2 + b^2 \]
\[ 72.25 = 16 + b^2 \]
\[ b^2 = 72.25 - 16 \]
\[ b^2 = 56.25 \]
Finally, we take the square root of both sides to find \( b \):
\[ b = \sqrt{56.25} \]
\[ b = 7.5 \]
So, the measure of the other side of the triangle is \( 7.5 \) meters.
Question A right triangle has a side length that measures 4 m and a hypotenuse that measures 8.5 m. What is the measure of the other side of the triangle? (1 point) Responses 7.5 m 7.5 m 8.1 m 8.1 m 9.4 m 9.4 m 9.8 m
1 answer
1 answer