Question

7.) a = 11 m
c = 15 m
b = ______

Explanation:

Assuming this is a right - triangle problem with \(c\) as the hypotenuse and \(a\), \(b\) as the legs, we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). We need to solve for \(b\), so we can re - arrange the formula to \(b = \sqrt{c^{2}-a^{2}}\).

Step 1: Identify the values and formula

We know that \(a = 11\space m\), \(c=15\space m\) and the formula from the Pythagorean theorem for a right triangle (assuming right - triangle) is \(b=\sqrt{c^{2}-a^{2}}\)

Step 2: Substitute the values into the formula

First, calculate \(c^{2}-a^{2}\). \(c^{2}=15^{2}=225\) and \(a^{2}=11^{2} = 121\). Then \(c^{2}-a^{2}=225 - 121=104\)

Step 3: Calculate the square root of 104

\(b=\sqrt{104}=\sqrt{4\times26} = 2\sqrt{26}\approx2\times5.1=10.2\space m\) (if we want a decimal approximation) or we can leave it as \(2\sqrt{26}\space m\)

Answer:

If we leave it in exact form, \(b = 2\sqrt{26}\space m\approx10.2\space m\) (the exact form is \(2\sqrt{26}\space m\) and the approximate decimal form is about \(10.2\space m\))