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Subducting oceanic slabs can plunge steeply or shallowly underneath the overriding plate.
In modern subduction zones the location of earthquakes can show how steeply the subducting slab is plunging into the mantle, however in ancient subduction zones we cannot use this technique.
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So let's go back and continue our example: Note there is only one answer in this case. When solving a "Side, Side, Angle" triangle we need to check if there could be another possible answer!
We know angle A (12 degrees) and the length of the opposite side (500. We want to know the length of the hypotenuse (H), so we will use the the formula for the sine: Substituting in the appropriate values, The S wave shadow zone is caused by the outer core not transmitting S waves. Here we have a right triangle with one 52.5 degree angle (half of 105 degrees) and a hypotenuse that is 6370 km long.
Instead, we can use the observation that a volcanic arc typically occurs above the point at which the subducting plate reaches a depth of 100 km.
If an ancient volcanic arc was 200 km from the trench that marks the initiation of subduction, what is the angle of subduction?