Answer:
7.7 km
Explanation:
Use cosine rule as here given two sides and one angle.
Cosine rule states:
a² = b² + c² - 2bc cos(A)
While solving, treat a = 7.5 km as to that opposite angle is given of 68°
then b = missing side, c = 5.2 km, A = 68°
Applying rule:
7.5² = b² + 5.2² - 2(b)(5.2) cos(68)
56.25 = b² + 27.04 - 3.8959b
56.25 - 27.04 = b² - 3.8959b
b² - 3.8959b = 29.21
b² - 3.8959b - 29.21 = 0
apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]
[tex]\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0[/tex]
[tex]\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}[/tex]
[tex]\sf b = 7.69 291 \quad or \quad b = -3.797[/tex]
[tex]\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)[/tex]
As length cannot be negative. Hence the value of b is only 7.7 km
