Question

find the measure of the hypotenuse in the right triangle abc.
a
24
45°
b
c
34.93
35.93
36.93
33.93

Explanation:

Step1: Identify triangle type

Triangle \( ABC \) is right - angled at \( B \) (since it's a right - triangle) and \( \angle C = 45^{\circ} \), so it's a 45 - 45 - 90 triangle (isosceles right - triangle), but we can also use trigonometric ratios. Let the hypotenuse be \( AC \), and the side \( AB = 24 \). We know that \( \sin C=\frac{AB}{AC} \).

Step2: Use sine formula

We know that \( \angle C = 45^{\circ} \) and \( AB = 24 \). The sine of \( 45^{\circ} \) is \( \sin(45^{\circ})=\frac{\sqrt{2}}{2}\approx0.7071 \). From \( \sin C=\frac{AB}{AC} \), we can re - arrange to get \( AC=\frac{AB}{\sin C} \). Substituting \( AB = 24 \) and \( \sin(45^{\circ})=\frac{\sqrt{2}}{2} \), we have \( AC=\frac{24}{\sin(45^{\circ})}=\frac{24}{\frac{\sqrt{2}}{2}}=24\times\frac{2}{\sqrt{2}} = 24\sqrt{2}\approx24\times1.4142 = 33.9408\approx33.93 \).

Answer:

\( 33.93 \) (the option with 33.93)