3. from an island, the titanic is 13 km away on a bearing of 80°.an iceberg is on a bearing of 125°from the titanic and 108° from the island. how far is the iceberg from the island?

9.61 km

Step-by-step explanation:

See image while seeing explanation

First we need to construct the figure, it is in the attached image.

Now we start to put the different angles, in order to solve the triangle.

Angle a is going to be the difference between 108° and 80°, giving 28°

The angle between the distance from the island and the Titanic, and the line that goes to the east is going to be 10° as we subtract 90° and 80°. We trace a line (Co) between Where the titanic is and the line that goes to the east so it has 90° degrees between Co and E, after this, we know that having the Titanic as the center, the angle is 180°, so we subtract 180° and 125° to have part of angle b, 55°. Now we need to find the rest of the angle b, so, knowing that all triangles' angles sum 180°, 180° - 90° + 10° = 80°, that is the missing part of b, now we add those two parts and have that b= 135°. Now we can solve the triangle by  setting up an equation system:

We know the values of A, a and b, therefore, we replace those values and solve the system. As it is a second order equation system, we will have 2 different pairs of solutions:

As a distance cannot be a negative number, we know that the proper solution is the second pair; in the triangle C is the distance between the island and the iceberg, givin 9.61 km

For part a. we need to find the total and apply the discount. The answer for part a is $71.

For part b. we need to subtract $3 from each individual price and then find the total. The answer for part b is $59.

Step-by-step explanation:

Part a: if each shirt is $12 and she wants to buy 3 shirts, then the cost will be 3 X $12 = $36.

If each pair of jeans is $19 dollars and she wants to buy two pairs, then the cost will be 2 x $19 = 38.

Add the two costs together to get the total cost of the purchase without the discount. $38 + $36 = $74.

Now subtract $3 from the total to get the answer for part a:

$74 - $3 = $71

Part b. If the original cost of the shirt is $12 and a $3 discount is applied to each shirt, each shirt will now cost $9. If Pani buys the three shirts at the discounted price, the cost of the shirts will be 3 x $9 = $27.

If the original cost of the jeans is $19 and a $3 discount is applied, the jeans will now cost $16. If Pani buys the two jeans at the discounted price, the cost will be 2 x $16 = $32.

Add the costs together to get the amount she would pay: $27 + $32 = $59.

hope this helps =)