Answer:
135.86≈ 136
Step-by-step explanation:
As Given in figure 1:
In ΔABC, m∠A = 72°, m∠B = 16° and c = 61 , where a, b, and c are lengths of side of ΔABC.
To find: Perimeter of triangle = ?
Sol: In ΔABC,
m∠A + m∠B + m∠C = 180° (sum of angles of a triangle)
m∠C = 180° - (72° + 16°)
m∠C = 92°
Now Using Sine Rule:
[tex]\frac{a}{SinA} = \frac{b}{SInB} = \frac{c}{SInC}[/tex]
[tex]\frac{a}{Sin 72^{\circ}} = \frac{b}{Sin 16^{\circ}} = \frac{61}{SIn92^{\circ}}[/tex]
Now, [tex]\frac{a}{sin72^{\circ}} = \frac{61}{Sin92^{\circ}}[/tex]
∴ [tex]a = \frac{61 \times Sin 72^{\circ}}{Sin92^{\circ}} = \frac{61 \times 0.951}{0.999} = \frac{58.011}{0.999} = 58.07[/tex]
In the same way, [tex]\frac{b}{sin 16^{\circ}} = \frac{61}{Sin92^{\circ}}[/tex]
∴ [tex]b = \frac{61 \times Sin 16^{\circ}}{Sin92^{\circ}} = \frac{61 \times 0.275}{0.999} = \frac{16.775}{0.999} = 16.79[/tex]
Therefore, a = 58.07 ≈ 58, b = 16.79 ≈ 17 and c = 61
Now, Perimeter of ΔABC = a + b + c = 58 + 17 + 61 = 136
