Question

in right triangle abc, side bc has a length of √533. the hypotenuse, side ab, has a length of 27. what is the value of sin b?

Explanation:

Step1: Find the length of side \(AC\)

Use the Pythagorean theorem \(AC=\sqrt{AB^{2}-BC^{2}}\). Substitute \(AB = 27\) and \(BC=\sqrt{533}\). Then \(AB^{2}=27^{2}=729\), \(BC^{2}=533\). So \(AC=\sqrt{729 - 533}=\sqrt{196}=14\).

Step2: Calculate \(\sin B\)

By the definition of sine in a right - triangle \(\sin B=\frac{AC}{AB}\). Since \(AC = 14\) and \(AB=27\), then \(\sin B=\frac{14}{27}\approx0.5185\)

Answer:

\(\frac{14}{27}\)