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In Delta QRS,s=4.2cm,mangle R=160^circ and mangle S=8^circ Find the length of r, to the nearest 10th of a centimeter. Answer Attemptiout of 2 r=square cm

Pergunta

In Delta QRS,s=4.2cm,mangle R=160^circ  and mangle S=8^circ  Find the length of r, to the
nearest 10th of a centimeter.
Answer Attemptiout of 2
r=square cm

In Delta QRS,s=4.2cm,mangle R=160^circ and mangle S=8^circ Find the length of r, to the nearest 10th of a centimeter. Answer Attemptiout of 2 r=square cm

Solução

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NúbiaProfissional · Tutor por 6 anos

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\(r = 24.1 \, cm\)

Explicação

## Step 1<br />We are given a triangle QRS with side s = 4.2 cm, angle R = 160°, and angle S = 8°. We are asked to find the length of side r.<br /><br />## Step 2<br />We can use the Law of Sines to solve this problem. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.<br /><br />### **The Law of Sines: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)**<br /><br />## Step 3<br />We can rearrange the Law of Sines to solve for side r:<br /><br />### **\(r = \frac{s \cdot \sin R}{\sin S}\)**<br /><br />## Step 4<br />Substitute the given values into the formula:<br /><br />### **\(r = \frac{4.2 \cdot \sin 160°}{\sin 8°}\)**<br /><br />## Step 5<br />Calculate the value of r using a calculator.
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