6.3
Applications of Right Triangle Trigonometry: Solving Right Triangles
591
a
15 ft
b
= 56º
EXAMPLE 2
Solving a Right Triangle Given an Angle and a Side
Solve the right triangle—find
a, b,
and
Solution:
S
TEP
1
Determine accuracy.
Since the given quantities, 15 ft and 56°, are both expressed
to two significant digits, we will round all calculated values to
two significant digits.
S
TEP
2
Solve for .
Two acute angles in a right triangle are complementary.
Solve for
S
TEP
3
Solve for a.Cosine of an angle is equal to the adjacent side over thehypotenuse.Solve for a.Evaluate the right side of the expression using a calculator.Round ato two significant digits.
Solve for bEvaluate the right side of the expression using a calculator.Round bto two significant digits.
.
5Check.Angles and sides are rounded to two significant digits.Check the trigonometric values of the specific angles by calculating the trigonometric ratios.
■
YOUR TURN
Solve the right triangle;
find
a
,
b
, and
u
.
aL8.4ftaL8.38789a=15cos56°cos56°=a15a=34°a.
a
+
56°
=
90°
a
.
Technology Tip
a
33 in.
b
37º
■ u=53°,a=26in.,

592
CHAPTER 6
Trigonometric Functions
Solving a Right Triangle Given the
Length of Two Sides
When solving a right triangle, we already know that one angle has measure 90°. Let us nowconsider the case when the lengths of two sides are given. In this case the third side can befound using the Pythagorean theorem. If we can determine the measure of one of the acuteangles, then we can find the measure of the third acute angle using the fact that the sum ofthe three angle measures in a triangle is 180°. How do we find the measure of one of theacute angles? Since we know the measure of the side lengths, we can use right triangle

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- Summer '17
- juan alberto
- Trigonometry, Right triangle, Inverse trigonometric functions