ST = 7.2
RT = 4.04
m∠S = 34°
Solution:
Given ΔRST is a right triangle.
RS = 6, ∠T = 56°
[tex]$\csc A=\frac{\text {Hypotenuse} }{\text {Opposite side}}[/tex]
[tex]$\csc A=\frac{ST}{RS}[/tex]
[tex]$\csc 56^\circ=\frac{ST}{6}[/tex]
[tex]$\csc 56^\circ \times 6=ST[/tex]
1.206 × 6 = ST
7.236 = ST
ST = 7.2
[tex]$\cot A=\frac{\text {Adjacent side} }{\text {Opposite side}}[/tex]
[tex]$\cot A=\frac{RT}{RS}[/tex]
[tex]$\cot 56^\circ=\frac{RT}{6}[/tex]
[tex]$\cot 56^\circ \times 6=RT[/tex]
0.674 × 6 = RT
4.044 = RT
RT = 4.04
To find the measure of angle S.
Sum of the interior angles of the triangle = 180°
m∠R + m∠S + m∠T = 180°
90° + m∠S + 56° = 180°
m∠S + 146° = 180°
m∠S = 180° – 146°
m∠S = 34°
