Question

The rangers at two park stations spot a signal flare at the same time. Based on the measurements shown in the diagram, what is the distance between park station 1 and the point where the flare was set off? Round to the nearest tenth. ​

Answer 1

The distance between park station 1 and the point where the flare was set off is 73.9 km.

What is distance?

Distance is the length between two points expressed in meters or kilometers.

To calculate the distance between park station 1 and the point where the flare was set off can be calculated using Sine Rule

Formula:

• a/sinA = b/sinB....................... Equation 1

Where:

• a = Distance between park station 1 and the point where the flare was set off.

Make a the subject of the equation

• a = bsinA/sinB............ Equation 2

From the diagram,

Given:

• A = 59°
• B = (180-59-75) = 46°
• b = 6.2 km

Substitute these values into equation 2

• a = 6.2(sin59°)/(sin46°)

• a = 73.9 km

Hence, the distance between park station 1 and the point where the flare was set off is 73.9 km.

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