Sketch a diagram describing the given situation, and then recall the definition of sine.
≈ 23.3 km
Practice makes perfect
We are given that a volcano has a magma reservoir located 15 kilometers beneath the bay, and we're asked to evaluate the length of a magma channel below the sea, which we will call l. We also know that the angle of elevation of a magma channel to the volcano is 40^(∘). Let's sketch a diagram for this situation.
Since the figure is a right triangle, we can use one of the trigonometric ratios to evaluate the value of l. Let's recall that the sine of ∠ A is the ratio of the leg opposite ∠ A to the hypotenuse. Using this definition, we can create an equation for sin 40^(∘).
sin 40^(∘)=15/l
Let's solve the above equation.
