Question

question: 11
triangle flr is similar to triangle mbt.
select all angles whose sine equals 12/37.
a. ∠b
b. ∠f
c. ∠l
d. ∠m
e. ∠r
f. ∠t

Explanation:

Step1: Recall the sine definition

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\triangle FLR\), \(\sin\angle R=\frac{FL}{FR}\). Given \(FL = 12\) and \(FR=37\), so \(\sin\angle R=\frac{12}{37}\).

Step2: Use the property of similar triangles

Since \(\triangle FLR\sim\triangle MBT\), corresponding angles are equal. \(\angle R\) in \(\triangle FLR\) corresponds to \(\angle T\) in \(\triangle MBT\) (because of the order of similarity \(FLR\sim MBT\), \(\angle F\) corresponds to \(\angle M\), \(\angle L\) corresponds to \(\angle B\), \(\angle R\) corresponds to \(\angle T\)).

Answer:

E. \(\angle R\), F. \(\angle T\)