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mojhsa [17]
3 years ago
15

forest ranger christ johnson at ranger station a sights a fire in teh direction 32 east of north. ranger rick thorpe at ranger s

tation b, 10 miles due east of a, sights the same fire on a line 48 west of north. find the distance from each ranger station to the fire.
Mathematics
1 answer:
RoseWind [281]3 years ago
4 0

Answer: 8.6 from Ranger Christ and 6.8 from Ranger Rick

Step-by-step explanation:

The sides of triangle with A point as Ranger christ, B point as Ranger rick and C point at which two fires intersect.

This can be better understood by using law of sines

\frac{sin(90-32)}{a}= \frac{sin(90-48)}{b}= \frac{sin(180-58-42)}{10}

Solving we get

a= 8.6

and b= 6.8

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Step-by-step explanation:

there is one central rectangle :

from (-4, 2) to (2, -2).

that means it dimensions are 6×4 (for x from -4 to +3, for y from +2 to -2).

and then there are 3 additional triangles

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(-4, -2) (2, -2) (2, -4)

(-6, 2) (-4, 2) (-4, -2)

with the leg lengths

(2, -4) to (2, 2) = 6, and (2, 2) to (6, 2) = 4

(-4, -2) to (2, -2) = 6, and (2, -2) to 2, -4) = 2

(-6, 2) to (-4, 2) = 2, and (-4, 2) to (-4, -2) = 4

the area of the rectangle is

6×4 = 24 square units

the area of the first triangle is

6×4/2 = 3×4 = 12 square units

the area of the second triangle is

6×2/2 = 6 square units

the area of the third triangle is

2×4 = 8 square units.

so, the total area is

24 + 12 + 6 + 8 = 50 square units.

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