Lesson 3.3: Solving Problems with Right Triangles

Lesson 3.3 video link here. (Video under development)

NOTE: An error in the explanation occurs at 26:55 to 28:39. The incorrect statement is Sine = Opposite/Adjacent and the subsequent calculations. Below are the correct calculations.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle indentalign=¨right¨»«mtext»tan§#160;§#952;=«/mtext»«mfrac»«mtext»opposite«/mtext»«mtext»adjacent«/mtext»«/mfrac»«mspace linebreak=¨newline¨/»«mi»tan«/mi»«mo»§#160;«/mo»«mn»6«/mn»«mo»§#176;«/mo»«mo»=«/mo»«mfrac»«mrow»«mn»100«/mn»«mo»§#160;«/mo»«mtext»m«/mtext»«/mrow»«mtext»d«/mtext»«/mfrac»«mspace linebreak=¨newline¨/»«mtext»d§#160;§#215;§#160;tan§#160;6§#176;«/mtext»«mo»=«/mo»«mn»100«/mn»«mo»§#160;«/mo»«mtext»m«/mtext»«mspace linebreak=¨newline¨/»«mtext»d§#160;=§#160;«/mtext»«mfrac»«mrow»«mn»100«/mn»«mo»§#160;«/mo»«mtext»m«/mtext»«/mrow»«mtext»tan§#160;6§#176;«/mtext»«/mfrac»«mspace linebreak=¨newline¨/»«mtext»d§#160;=§#160;951.4364454...«/mtext»«mspace linebreak=¨newline¨/»«mtext»d§#160;=§#160;951.4§#160;m§#160;«/mtext»«/mstyle»«/math»

The three primary trigonometric ratios are important tools for determining unknown values in a right triangle. In this lesson, you will use these ratios to solve more complex problems.


In Lesson 3.3, you will learn about

  • solving right triangles

  • solving problems that involve more than one right triangle

 

Warm Up

A. The Pythagorean Theorem

For a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. This relationship is often referred to as the Pythagorean theorem or Pythagoras' theorem, and is named after a Greek mathematician who lived about 2500 years ago.

The Pythagorean theorem can be used to determine the length of an unknown side of a right triangle.

Example 1

A right triangle has a hypotenuse length of 15 m and a leg length of 12 m. Determine the length of the triangle's other leg.