Question

Use the geometric mean (leg) theorem to find the value of 'a' given the following information:

```
b = 0.072
h = 0.2770
a = ?
```
a) 0.205
b) 0.070/5
c) 14
d) 0.072
e) 0.02770
f) 6

Answer 1

After calculating the geometric mean using the provided values, it appears there may have been a typo in the question since the result does not match any of the given options. Assuming a typo with the value of 'b', option (e) is the closest.

Step-by-step explanation:

The student's question asks to find the value of 'a' using the geometric mean (leg) theorem. According to this theorem, in a right triangle, the length of the altitude on the hypotenuse (a) is the geometric mean of the segments of the hypotenuse (which are b and h in this case) when the hypotenuse is divided by the altitude. The geometric mean (leg) theorem is expressed as a = sqrt(b * h).

Given that b = 0.072 and h = 0.2770, we can calculate 'a' by substituting the provided values into the geometric mean formula:

a = sqrt(0.072 * 0.2770) = sqrt(0.019944) ≈ 0.1412

The answer is not included in the given options. However, the closest to 0.1412 is option (e) 0.02770 if we assume there was a typo in the question and the actual value of 'b' was meant to be 0.00277 instead of 0.072.