Question

calculator
what is the length of \\\\(\overline{st}\\\\), to the nearest tenth of a yard?
\\(\circ\\) 3.6 yd
\\(\circ\\) 6.1 yd
\\(\circ\\) 6.9 yd
\\(\circ\\) 8.0 yd
(image of triangle str with sr = 7 yd, angle at r is 59°, angle at t is 79°)

Explanation:

Step1: Find angle at S

In triangle \( STR \), the sum of angles in a triangle is \( 180^\circ \). So, \( \angle S = 180^\circ - 59^\circ - 79^\circ = 42^\circ \).

Step2: Apply Law of Sines

The Law of Sines states that \( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \). Here, we have \( \frac{ST}{\sin R}=\frac{SR}{\sin T} \). We know \( SR = 7 \) yd, \( \angle R = 59^\circ \), \( \angle T = 79^\circ \). So, \( ST=\frac{SR \cdot \sin R}{\sin T} \).
Substitute the values: \( ST=\frac{7 \cdot \sin 59^\circ}{\sin 79^\circ} \).
Calculate \( \sin 59^\circ \approx 0.8572 \), \( \sin 79^\circ \approx 0.9816 \).
Then \( ST=\frac{7 \cdot 0.8572}{0.9816} \approx \frac{5.9904}{0.9816} \approx 6.1 \) yd.

Answer:

B. 6.1 yd