SOLUTION: The swim portion of a triathlon follows a triangular path. The swimmers start by swimming to a buoy that is placed 900m from the starting point at an angle of N15° E. Upon reaching
Algebra ->
Test
-> SOLUTION: The swim portion of a triathlon follows a triangular path. The swimmers start by swimming to a buoy that is placed 900m from the starting point at an angle of N15° E. Upon reaching
Log On
Question 1036914: The swim portion of a triathlon follows a triangular path. The swimmers start by swimming to a buoy that is placed 900m from the starting point at an angle of N15° E. Upon reaching the buoy, the swimmers change their heading to E30° S and swim another 1200m. Finally they return to the starting point and jump on their Bikes. How long was the swim in total?
Please solve this ASAP! I have tried but it is very difficult to punch in. Sorry about that!
You can put this solution on YOUR website! We have a triangle with angles A, B, and C, and sides a, b, c.
One side is 900m. Find the other 2 sides
The angles of every triangle add up to 180 degrees
A+B+C = 180º
15+30 = 45
180-45 = 135 degrees is your third angle. Let's call them:
A = 15
B = 30
C = 135
And the sides, we'll call side b = 900m.
``````````````````````````````````````````
The sine rule says:
a/sinA = b/sinB = c/sin C
``````````````````````````````
Let's first find side c:
c/sinC = b/sinB Multiply both sides times sinC:
c = bsinC/sinB
= 900sin135/sin30 Use your calculator and you get:
= 1272.79 is side c
```````````````````````````````
Let's find side a:
a/sinA = b/sinB
a = bsinA/sinB
900sin15/sin30
= 465.87 is your third side
``````````````````````````````````
How long was the swim?
900+1272.79+465.87 = 2638.66 meters.
See the picture I made you below
John
