Question

A ship is located at point X represented in the figure above. An island is located at point Y and the angle between the ship's route and the island is 96∘ as shown. After travelling 129 kilometers to point Z, the distance between the ship and the island is measured to be 465 kilometers. What is the measure, in degrees, of ∠ZYX?

Answer 1

The measure, in degrees, of ∠ZYX, given that the angle between the ship's route and the island is 96°, is 16.0°

How to calculate the measure, in degrees, of ∠ZYX?

From the diagram given (See attached photo), The following items were discovered:

• Side x = 465 kimometers
• Angle X = ∠ZXY = 96 degrees
• Side y = 129 kilometers
• Angle Y = ∠ZYX =?

From the above information, we can use sine rule to calculate the measure of ∠ZYX. This is shown below:

`(x)/(Sine\ X) = (y)/(Sine\ Y) \\\\(465)/(Sine\ 96) = (129)/(Sine\ \angle ZYX)\\\\Cross\ multiply\\\\465\ *\ Sine\ \angle ZYX = 129\ *\ Sine\ 96 \\\\Sine\ \angle ZYX = (129\ *\ Sine\ 96)/(465) \\\\Sine\ \angle ZYX = 0.2759\\\\\angle ZYX = Sine^(-1)\ (0.2759)\\\\\angle ZYX = 16.0\ \textdegree\\\\`

Complete question:

See attached photo