Question

Foundations for College Mathematics, Grade 11 Unit III Workbook 4 For the following questions you will need to create your own diagrams. 7. Two islands A and B are 3 km apart. A third island C is located due south of A and due west of B. From island B the angle between islands A and C is 33

Calculate how far island C is from island A and from island B.

Answer 1

To find the distance between island C and island A, we can create a right triangle and use sine to solve for the distance. The distance between island C and island B is equal to the distance between island A and island B, which is 3 km.

Step-by-step explanation:

To find the distance between island C and island A:

Since the angle between islands A and C is given as 33°, we can create a right triangle with island A as the hypotenuse. The side opposite the angle of 33° is the distance between island C and island A. We can use the trigonometric function sine to solve for this distance.

Sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

sin(33°) = opposite/hypotenuse

We know that the hypotenuse (distance between island A and island B) is 3 km.

Therefore, the distance between island C and island A is sin(33°) * 3 km.

To find the distance between island C and island B:

Since island C is located due west of island B, and the distance between islands A and B is 3 km, the distance between island C and island B is also 3 km.

Therefore, the distance between island C and island A is sin(33°) * 3 km, and the distance between island C and island B is 3 km.