Post on 22-Dec-2015
Solving Right Triangles
• Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the triangle.
• All of the following examples will use degree measure, so set the mode on your calculator to degree.
c
7 in
a
62
Example 1:Solve the given triangle:
First, solve for θ.
Since the sum of the two acute angles in a right triangle is 90°, we have …
So θ is 28°.
62 90 28
c
7 in
a
62
Now solve for c, which is the hypotenuse.
The side measured 7 in. is the side adjacent to the given 62° angle.
The trigonometric ratio using adjacent and hypotenuse is cosine.
cos 62adj
hyp
c
7 in
a
62
cos 62adj
hyp 7
c
cos 62
7c 14.91
The value of c is approximately 14.91 inches.
c
7 in
a
62
Last, solve for a, which is the side opposite the 62° angle.
The side measured 7 in. is the side adjacent to the given 62° angle.
The trigonometric ratio using opposite and adjacent is tangent.
tan 62opp
adj
c
7 in
a
62
tan 62opp
adj
7
a
7 tan 62a 13.17
The value of a is approximately 13.17 inches.
84.7 cm
62.3 cm
b
Example 2:Solve the given triangle:
First, solve for θ.
Since the hypotenuse and the side adjacent to θ are given, use cosine.
84.7 cm
62.3 cm
b
So θ is approximately 42.6°.
adjcos
hyp 62.3
84.7 0.736
1cos 0.736 42.6
Now solve for α.
84.7 cm
62.3 cm
b
Since the sum of the two acute angles in a right triangle is 90°, we have …
So α is approximately 47.4°
90
42.6 90
47.4
Last, solve for b, which is the side opposite θ.
The side measured 62.3 in. is the side adjacent to θ
The trigonometric ratio using opposite and adjacent is tangent.
tan 42.6opp
adj
84.7 cm
62.3 cm
b
62.3
b
62.3 tan 42.6b 57.3
The value of b is approximately 57.3 cm.
tan 42.6opp
adj
84.7 cm
62.3 cm
b
Note that we could have used the Pythagorean Theorem to solve for side b.