Download Lecture Notes for Section 2.4

Trigonometry Lecture Notes
Section 2.4
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Section 2.4: Solving Right Triangles
Big Idea: You can use trig functions and their definitions to compute missing measurements on
a right triangle.
Big Skill: You should be able to “solve” right triangles by computing missing measurements and
stating your answers to the correct number of significant digits.
The way we write a measurement can be used to indicate how precise the measurement was.
o If we write 15 inches, that means the object we measured was between 14.5 and 15.5
inches long.
o If we write 15.0 inches, that means the object we measured was between 14.95 and 15.05
inches long.
o If we write 15.00 inches, that means the object we measured was between 14.995 and
15.005 inches long.
o In other words, a measurement is good to  ½ of the least significant digit.
This is called using significant digits to write a number.
When using trig functions, the rules for writing significant digits are as follows:
Angle Precision
1
0.1 or 10
0.01 or 1
0.001 or 10
Angles and Accuracy of Trig Functions
Trig Function Accuracy
Example
2 sig. figs.
sin17  0.29 , tan85  11
3 sig. figs.
sin1.1  0.0192 ,
cos520'  0.996
4 sig. figs.
cos 45.00  0.7071 ,
tan8013'  5.799
5 sig. figs.
cos 45.000  0.70711 ,
tan801320  5.8028
To solve a right triangle:
1. Make a sketch of the triangle, label sides and angles consistently (a, b, and c for the legs
and hypotenuse; A and B for the complementary angles), and label the given information.
2. Find a way to relate the unknown parts to the given information using:
a. a trig function (sine, cosine, or tangent),
b. the Pythagorean Theorem (a2 + b2 = c2),
c. or complementary angles.
d. Try to use original given information to minimize rounding errors.
3. Check your work:
a. Make sure the sides obey the Pythagorean Theorem.
b. Make sure the angles add up to 180.
c. Make sure unused trig functions give the right answers.
d. Make sure that the longest side is opposite the largest angle, and the shortest side
is opposite the smallest angle.
Trigonometry Lecture Notes
Section 2.4
Practice:
1. Solve a right triangle given two legs:
2. Solve a right triangle given a leg and a hypotenuse:
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Trigonometry Lecture Notes
Section 2.4
3. Solve a right triangle given an angle and an adjacent side:
4. Solve a right triangle given an angle and an opposite side:
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Trigonometry Lecture Notes
Section 2.4
5. Solve a right triangle given an angle and the hypotenuse:
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