Math project. It is EVIL :D

1. The Fireman Question

2. 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).

3. 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.

4. What do we know?
1. The hotel is 4.2 km away
2. 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.

5. 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.

6. 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

7. 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 = 49
a=7

8. 1. Tan=
2. Solve for the missing
side…
c2 = a2 + b2
c2 = (-5)2 + 122
c2 = 169
C = 13

10. is our answer in radians!

11. 1. This is our formula
2. 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.

12. 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!

13. 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.