     Home Right Triangles Angles in Standard Position Sine Law & Ambiguous Case Cosine Law Problem Solving Summary&Test UNIT 6  : BASIC TRIGONOMETRY WITH TRIANGLES

LESSON 1:  SOLVING RIGHT TRIANGLES

Pythagorean Theorem:

In any right triangle, the square on the hypotenuse [c] equals the sum of the squares on the other two sides [a,b].  Primary Trigonometric Ratios :    Example 1:

Find the six trigonometric ratios for < P in fraction form and in decimal form (nearest hundredth). Solution:

First calculate the hypotenuse using the Pythagorean Theorem.  Example 2:  Right Triangles – finding a side

CASE 1:  Given a right triangle with one side and one angle known.

Find side “x” in the right triangle below.

 Solution: x = side opposite  and  14.4 = side adjacent relative to 42o.  Hence we use the tangent ratio since it involves opposite and adjacent.  Example 3: Right Triangles – finding an angle

CASE 2:  Given a right triangle with two sides  known.

Find < A  in the right triangle below.

 Solution:   15.9 = hypotenuse  and  12.3 = side adjacent relative to    Example 4: Solving Right Triangles – Finding all unknown sides and angles.  Solution:  Find side “a” first.

a = side opposite  and    8.4 = side adjacent relative to 38o.  Hence we use the tangent ratio since it involves opposite and adjacent. To find “c”, we could use either trigonometry as above or Pythagoras. Example 5: Right Triangles – Two Triangle Questions.

Find DG to the nearest tenth in the diagram below. Solution: We must use the triangle with 3 elements known.  Hence we first find side DF in this triangle. 