Question

Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!

Answer 1

The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.

Distance of each truck from the fire

Using sine rule, we find the length of AB and BC as shown in the image.

a/sin A = b/sin B = c/sin C

Angle C = 180 - (58 + 52) = 70⁰

1.3/(sin 70) = b/(sin 52)

b = (1.3sin 52) / (sin 70)

b = 1.09 mile

c = (1.3sin 58) / (sin 70)

c = 1.1732 miles

Bisect angle C, and use sine rule again to find the lengths of bisected line AB.

1.09/(sin 90) = x/[sin (90 - 58)]

1.09/(sin 90) = x/(sin 32)

x = (1.09 sin 32)/(sin 90)

x = 0.578 mile

Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile

Learn more about sine rule here: brainly.com/question/27174058

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