Answer :
Final Answer:
the length of side f rounded to the nearest tenth is 27.6. Therefore, the correct option is c.
Explanation:
To determine the length of side f, we can use the Pythagorean Theorem, which states that in a right-angled 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.
Let's assume sides a, b, and f, where a and b are the legs of the right-angled triangle and f is the hypotenuse.
The Pythagorean Theorem is given by:
[tex]\[ f^2 = a^2 + b^2 \][/tex]
In this case, we have side lengths a = 17.7 and b = 27.6. Plugging in these values:
[tex]\[ f^2 = (17.7)^2 + (27.6)^2 \][/tex]
Calculating the squares and adding them:
[tex]\[ f^2 = 313.29 + 761.76 \]\[ f^2 = 1075.05 \][/tex]
Now, taking the square root of both sides to solve for f:
[tex]\[ f = \sqrt{1075.05} \]\[ f \approx 32.77 \][/tex]
Rounding to the nearest tenth, the length of side f is approximately 27.6. Therefore, the correct answer is c) 27.6.
