Question

3.1 mm
1.6 mm
what is the length of the missing leg? if necessary, round to the nearest tenth.
a = millimeters

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( c^2 = a^2 + b^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, hypotenuse \( c = 3.1 \) mm, one leg \( b = 1.6 \) mm, find \( a \). Rearrange formula: \( a^2 = c^2 - b^2 \).

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

\( c^2 = 3.1^2 = 9.61 \), \( b^2 = 1.6^2 = 2.56 \). So \( a^2 = 9.61 - 2.56 = 7.05 \).

Step3: Find \( a \)

Take square root: \( a = \sqrt{7.05} \approx 2.655 \), round to nearest tenth: \( 2.7 \).

Answer:

2.7