Question

in the right triangle shown, which of the following is closest to the value of c?
note: figure not drawn to scale.
7.7
10.8
58.5
15

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 6\), \(b = 9\). So \(c=\sqrt{6^{2}+9^{2}}\).

Step2: Calculate \(6^{2}+9^{2}\)

\(6^{2}=36\), \(9^{2}=81\). Then \(6^{2}+9^{2}=36 + 81=117\).

Step3: Calculate \(\sqrt{117}\)

\(\sqrt{117}\approx10.8\) (since \(10^{2}=100\) and \(11^{2}=121\), and \(10.8^{2}=(10 + 0.8)^{2}=100+16 + 0.64=116.64\approx117\))

Answer:

10.8