Answer:
see explanation
Step-by-step explanation:
Using the sine ration on the left, right triangle
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × sin35° = a , thus
a ≈ 4.93 cm
a + b = 15.7, so
4.93 + b = 15.7 ( subtract 4.93 from both sides )
b = 10.77
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Using the cosine ratio on the left, right triangle
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × cos35° = y , so
y ≈ 7.04 cm
Using Pythagoras' identity on the right, right triangle
c² = b² + y² = (10.77)² + (7.04)² = 115.99 + 49.56 = 165.55
Take the square root of both sides )
c = [tex]\sqrt{165.55}[/tex] ≈ 12.87 cm
