Question

on the star map, three stars form a right triangle with star vega at the right angle. the distance between vega and deneb is 6 centimeters. the distance between deneb and altair is 11 centimeters. round your answer to the nearest tenth. the distance between vega and altair on the star map is about centimeters.

Explanation:

Step1: Apply Pythagorean theorem

Let the distance between Vega and Deneb be \(a = 6\), the distance between Deneb and Altair be \(c = 11\), and the distance between Vega and Altair be \(b\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 6\) and \(c = 11\) into the formula: \(b=\sqrt{11^{2}-6^{2}}=\sqrt{121 - 36}=\sqrt{85}\).

Step3: Calculate the value

\(\sqrt{85}\approx9.2\) (rounded to the nearest tenth).

Answer:

\(9.2\)