Question

1. (l78) find the length of the missing side for the right triangle (an irrational answer should be estimated to two decimal places).

a) 9.07
b) 10.00
c) 11.23
d) 12.79
e) 13.42

1. (l78) find the length of the missing side for the right triangle (an irrational answer should be estimated to two decimal places).

a) 35.61
b) 36.51
c) 37.51
d) 35.51
e) 35.71

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\) (when \(c\) is the hypotenuse) or \(a^{2}=c^{2}-b^{2}\) (when \(a\) is a non - hypotenuse side).

Step2: Solve problem 11

Let \(a = 6\) and \(b = 8\). We want to find the hypotenuse \(c\). Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Step3: Solve problem 12

Let \(a\) be the missing side, \(b = 35\) and \(c = 50\). Since \(c\) is the hypotenuse, \(a=\sqrt{c^{2}-b^{2}}=\sqrt{50^{2}-35^{2}}=\sqrt{(50 + 35)(50 - 35)}=\sqrt{85\times15}=\sqrt{1275}\approx35.71\).

Answer:

1. B. 10.00
2. E. 35.71