Given:
Given that RST is a right triangle.
The measure of ∠R is 35°.
The length of ST is 12 units.
The length of the hypotenuse is t units.
We need to determine the value of t.
Value of t:
The value of t can be determined using the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
where [tex]\theta=R[/tex], the side opposite to ∠R is ST and hypotenuse is SR.
Substituting these values, we get;
[tex]sin \ R=\frac{ST}{SR}[/tex]
Substituting ST = 12 and SR = t, we get;
[tex]sin \ 35^{\circ}=\frac{12}{t}[/tex]
Simplifying, we get;
[tex]t=\frac{12}{sin \ 35^{\circ}}[/tex]
[tex]t=\frac{12}{0.574}[/tex]
[tex]t=20.9[/tex]
Thus, the value of t is 20.9 units.
