2 Answers

Zeliax · Answer 1 · 2023-08-20T13:31:42+0000

Answer:

843 m (nearest metre)

Explanation:

As the triangle is not a right triangle, we need to use the cosine rule to find the length of x.

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where:

From inspection of the diagram:

Substitute these values into the formula and solve for x:

$\implies c^2=a^2+b^2-2ab \cos C$

$\implies x^2=760^2+470^2-2(760)(470) \cos 82^(\circ)$

$\implies x^2=798500-714400 \cos 83^(\circ)$

$\implies x=\sqrt{798500-714400 \cos 83^(\circ)}$

$\implies x=843.4669769...$

$\implies x=843 \sf \:m\:\:(nearest\:metre)$

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