Question

A fireman is heading towards a forest fire and needs to know how far away the fire is. The person in the fire tower can determine the distance and the angle shown below. What is the distance from the fireman to the fire? Show your work.

Answer 1

The distance from the fireman and the fire is 3.83 miles.

Using the values given, we can calculate the distance using pythagoras ;

• distance = √opposite² + adjacent²

Inputting the values into the formula ;

distance = √2.1² + 3.2²

distance = √14.65

distance = 3.8275318418

Therefore, the distance between the fireman and the fire is 3.83 miles.

Answer 2

Answer: 3.82 miles

Explanation:

According to the shown figure, we can imagine the scene as a right triangle, where the tower is located at the right angle, and the fireman and the forest fire located at each of the other two vertices.

So, since we are dealing with a right triangle we can use the Pithagorean Theorem, in order to find the distance from the fireman to the fire
`d`, which is also the hypotenuse.

`d^(2)= (2.1 miles)^(2) +(3.2 miles)^(2)`

`d=\sqrt{(2.1 miles)^(2) +(3.2 miles)^(2)}`

Finally:

`d=3.82 miles`