The Fireman Question

Set fire to a prominent hotel 4.2 km away from the nearest fire station in order to lure the firemen away from their precious puppy. We will set fire to the busiest part of the hotel, the lobby. The area that we want to go up in flames is equivalent to the sector of cos(α+β).

1. How long will it take the firemen to drive to the burning hotel if they drive at a constant speed of 50km/h.

2. If cos a > 0 and sin B <0, sin α is 24/25 and tan β is -5/12, find the angle at which the catapult will throw our fireball.

3. Find the area that the fire will burn assuming it starts burning from the origin if you were to compare it to the Cartesian plane.

What do we know?1. The hotel is 4.2 km away2. They will be driving at a constant speed of 50 km/h.

What do we have to do?1. Use the speed, time formula to figure out how long it will take for the firemen to drive to the hotel.

1. This is our formula

2. Time to plug it in!

3. The Km’s reduce and we are left with hours.

4. Time to convert from hours to minutes!

5. We multiply by 60 because that’s how many minutes there are in an hour.

Here’s what we have to do

• First: Draw our triangles (sin α and tan β)

• Second: Solve for cos (α + β)

• Third: Convert our answer from radians to degrees

Remember SOHCAHTOA? Sin=

1. That means 24 is going to be the “opposite” side and 25 is going to be our hypotenuse!

2. Now let’s figure out the missing side! a2 = c2 – b2

a2 = 252 – 242

a2 = 49a = 7

1. Tan=

2. Solve for the missing side…

c2 = a2 + b2

c2 = (-5)2 + 122

c2 = 169

C = 13

is our answer in radians!

1. This is our formula2. Let’s plug in our answer

from the last slide!3. Now cross multiply

4. To get D by itself divide both sides by π. This is the exact answer, use it for any further calculations!

5. This is the non- exact answer. We can understand 35.9461 degrees a lot easier then 112.9846/ π.

1. This is the formula for the area of a circle.

2. Time to… plug it in!

3. Now all you have to do is solve, remember to use BEDMAS!

4. Tada! The answer!

It will take the firemen 10.08 minutes to drive to the burning hotel and back.

Our catapult throws at an angle of approximately 36 degrees.

Approximately 5 m2 of the hotel will burn.