I have to determine the unknown length of a right triangke to the nearest tenth of a unit. One side is 7m and the base is 10m. I got a friend to do this and age came up with 7.1m as the answer. When I do the steps I get the answer 12.21. I believe my friend is right but need help with the steps on how to figure this out. Thank you!
Pythagorean Theorem
a^2 + b^2 = c^2
7^2 + 10^2 = c^2
49 + 100 = c^2
149 = c^2
12.21 = c
Pythagorean theorem
side^2 + side^2 = hypotenuse^2
7^2 + 10^2 = 49 + 100 = 149
I would agree with you.
To determine the unknown length of the right triangle, you can use the Pythagorean Theorem, which 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 other two sides.
In this case, the side given with a length of 7m is one of the legs of the triangle, and the base with a length of 10m is the other leg. Let's label the unknown length as "x" (in meters).
Using the Pythagorean Theorem, we can write the equation as follows:
x^2 = 7^2 + 10^2
Simplifying:
x^2 = 49 + 100
x^2 = 149
Now, to find the value of "x," we need to take the square root of both sides of the equation, since we want to solve for "x" and not "x squared."
√(x^2) = √149
Taking the square root:
x = √149
Approximating √149 to the nearest tenth, we get:
x ≈ 12.2 (rounded to one decimal place)
Hence, the unknown length of the right triangle, to the nearest tenth, is approximately 12.2m.
Based on your friend's answer of 7.1m, it seems like they made an error in the calculation.