Answer:
843 m (nearest metre)
Step-by-step explanation:
As the triangle is not a right triangle, we need to use the cosine rule to find the length of x.
Cosine rule
[tex]c^2=a^2+b^2-2ab \cos C[/tex]
where:
- C is the angle
- c is the side opposite the angle
- a and b are the sides adjacent to the angle
From inspection of the diagram:
- C = 83°
- c = x
- a = 760
- b = 470
Substitute these values into the formula and solve for x:
[tex]\implies c^2=a^2+b^2-2ab \cos C[/tex]
[tex]\implies x^2=760^2+470^2-2(760)(470) \cos 82^{\circ}[/tex]
[tex]\implies x^2=798500-714400 \cos 83^{\circ}[/tex]
[tex]\implies x=\sqrt{798500-714400 \cos 83^{\circ}}[/tex]
[tex]\implies x=843.4669769...[/tex]
[tex]\implies x=843 \sf \:m\:\:(nearest\:metre)[/tex]
