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Tangent Ratio

Source: Winding Road - Wenjie Dong/E+/Getty Images

Introduction

Aqueduct

Aqueduct.

Sources: Aqueduct - Bertl123/iStock/Getty Images;

Passenger Train - Leonid Andronov/iStock/Getty Images

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Lesson Goals

  • Compute the tangent ratio for an acute angle in a right-angled triangle given the side lengths.
  • Use the tangent ratio to solve for an unknown side length in a right-angled triangle.
  • Use the inverse tangent operation on your calculator to solve for an interior angle in a right-angled triangle.

Try This

A hockey player shoots a puck towards an open net \(5.5\) m away. The net is \(1.2\) m tall. If the puck comes off of the ice, what is the maximum angle that it can make with the ice and still go in the net? (Assume that the puck travels quickly enough that we can ignore the effects of gravity.)

Hockey player 5.5 metres from a 1.2 metre tall net.

Source: Hockey Player - aarrows/iStock/Getty Images