a We are asked to find how many meters the submarine must lower to pass under the iceberg if it is 4000 meters ahead, with an angle of depression of 34^(∘) to the bottom of the iceberg. Let's draw a diagram of this situation. We will call the vertical distance x.
Notice that we can use one of the trigonometric ratios to evaluate the value of x. Let's recall that in a right triangle the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent this angle. Using this definition, we can create an equation for tan 34^(∘).
tan 34^(∘)=x/4000
Let's solve the above equation.
The submarine must lower approximately 2698 meters to pass under the iceberg.
b In this part we want to find how many meters the submarine must rise to pass over the sunken ship if it is 1500 m ahead, with an angle of elevation of 19^(∘) to the highest part of the sunken ship. Let's draw a diagram of this situation. We will call the vertical distance x.
Notice that we can use one of the trigonometric ratios to evaluate the value of x. Again let's recall that in a right triangle the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent this angle. Using this definition, we can create an equation for tan 19^(∘).
tan 19^(∘)=x/1500
Let's solve the above equation.
