The length of AC is 11.4 centimeters and the length of BC is 30.9 centimeters.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a triangle.
ΔABC and ΔACD are two triangles.
A. The value of AC will be
Using the cosine rule,
AC² = AD² + AC² - 2 × AD × AC × cos D
AC² = 17² + 13² - 2 × 17 × 13 × cos 42
AC² = 289 + 169 - 328.47
AC² = 129.52
AC = 11.4 cm
B. The value of BC will be
Using the sine rule,
[tex]\rm \dfrac{BC}{sin A} = \dfrac{CA}{sin B} = \dfrac{AB}{sin C}\\\\\dfrac{BC}{sin 76} = \dfrac{11.4}{sin 21 } =\dfrac{AB}{sin 83 }[/tex]
From the first 2, we have
[tex]\rm \dfrac{BC}{sin 76} = \dfrac{11.4}{sin 21 } \\\\B \ C \ \ = 30.9[/tex]
Thus, the length of AC is 11.4 centimeters and the length of BC is 30.9 centimeters.
More about the trigonometry link is given below.
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