Question

Towers A and B are located 5 miles apart. A ranger spots a fire at a 42-degree angle from tower A. Another fire ranger spots the same fire at a 64-degree angle from tower B. To the nearest tenth of a mile, how far from tower B is the fire?

Answer 1

3.5 miles

Explanation:

(Assuming the height of Tower A = that of Tower B)

1) How far is Tower B from the fire (in terms of x)?

First, let's note the height of building B (and A) as x. Using a trigonometric table, we can see that the tan(64)=2.0503, and after multiplying by x to find the distance to the fire, it gives us 2.0503x.

2) How far is Tower A from the fire (in terms of x)?

Using a trigonometric table, we can see that the tan(42)=0.9004, and after multiplying by x to find the distance to the fire, it gives us 0.9004x

3) What's next?

Now that we know how far both towers are away from the fire, we can start to calculate the mileage. Adding the two numbers we've gotten so far leads us to 2.0503x+0.9004x=5, 2.9507x=5, x=1.6945. Then, to find the actual distance of B to the fire, we multiply 2.0503 by 1.6945 to get 3.4742 or when rounded to the 100ths, 3.5.

Hopefully I used the right angle :D

If I didn't, you can just tell me to do it again