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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 <A. Hence we use the
cosine ratio since it involves hypotenuse and adjacent.
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.