Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
( a = square ) centimeters
(there is a right triangle image with hypotenuse 8.9 cm, one leg 8.7 cm, and the other leg labeled ( a ))

Explanation:

Step1: Identify the triangle type

This is a right triangle, so we use the Pythagorean theorem: \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, \( c = 8.9 \) cm, \( b = 8.7 \) cm, and we need to find \( a \). Rearranging the formula: \( a^2 = c^2 - b^2 \).

Step2: Calculate \( c^2 - b^2 \)

Substitute the values: \( c^2 = 8.9^2 = 79.21 \), \( b^2 = 8.7^2 = 75.69 \). Then \( a^2 = 79.21 - 75.69 = 3.52 \).

Step3: Find \( a \)

Take the square root: \( a = \sqrt{3.52} \approx 1.876 \), round to the nearest tenth (or as needed, here likely to one decimal or whole? Wait, let's check calculation again. Wait, 8.9 squared: 8.98.9: 88=64, 80.9=7.2, 0.98=7.2, 0.9*0.9=0.81; (8+0.9)^2=64 + 14.4 + 0.81=79.21. 8.7 squared: (8+0.7)^2=64 + 11.2 + 0.49=75.69. 79.21 -75.69=3.52. Square root of 3.52: √3.52 ≈ 1.876, which is approximately 1.9 (if rounding to nearest tenth) or 2? Wait, maybe the problem expects rounding to nearest tenth. Wait, let's compute √3.52:

3.52^(1/2) ≈ 1.876, so approximately 1.9 cm (nearest tenth) or 2 cm (nearest whole). Wait, maybe the problem has a typo? Wait, no, maybe I misread the sides. Wait, the hypotenuse is 8.9, one leg is 8.7, so the other leg is very short. Wait, let's confirm the Pythagorean theorem again. Yes, \( a = \sqrt{c^2 - b^2} = \sqrt{8.9^2 - 8.7^2} = \sqrt{(8.9 - 8.7)(8.9 + 8.7)} = \sqrt{0.2 * 17.6} = \sqrt{3.52} ≈ 1.876 \), so approximately 1.9 cm (if rounding to nearest tenth) or 2 cm (nearest whole). But maybe the problem wants to the nearest tenth, so 1.9, or maybe the original numbers are different? Wait, maybe I made a mistake. Wait, 8.9 and 8.7: the difference in squares is 3.52, square root is ~1.876, so approximately 1.9 cm.

Answer:

\( \boxed{1.9} \) (or \( \boxed{2} \) if rounding to nearest whole, but 1.9 is more accurate to nearest tenth)