Question

use the information given in the figure to find the length rv. if applicable, round your answer to the nearest whole number. the lengths on the figure are not drawn accurately.

Explanation:

Step1: Apply the Pythagorean theorem

In right - triangle \(RVS\), according to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = RS = 57\) and \(a = VS\). First, find \(VS\) from right - triangle \(TVS\). In right - triangle \(TVS\), \(TV=\sqrt{TS^{2}-VS^{2}}\), but we can also use the fact that in right - triangle \(RVS\), let \(RV = x\), \(VS\) can be found from right - triangle \(RVS\) using \(RV=\sqrt{RS^{2}-VS^{2}}\). Wait, another way: since \(UV = 36\) (given) and in a rhombus (assuming it's a rhombus - like figure with perpendicular diagonals), \(VS=UV = 36\) (diagonals bisect each other perpendicularly).
In right - triangle \(RVS\), by the Pythagorean theorem \(RV=\sqrt{RS^{2}-VS^{2}}\).

Step2: Substitute the values

Given \(RS = 57\) and \(VS = 36\). Then \(RV=\sqrt{57^{2}-36^{2}}=\sqrt{(57 + 36)(57 - 36)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)).
\(=\sqrt{93\times21}=\sqrt{1953}\approx44.19\approx44\)

Answer:

\(44\)