Do Now
• Answer the following by using your trig chart or
your calculator.
1. 𝑠𝑖𝑛136°
3. 𝑐𝑜𝑠𝜃 =
2. 𝑡𝑎𝑛60°
3
2
4. 𝑠𝑖𝑛30°
5. tan𝜃 = 1.05
6. 𝑐𝑜𝑠𝜃 = .4216
7. 𝑠𝑒𝑐𝜃 = 2
8. 𝑐𝑜𝑡𝜃 = 5.48
Section 2.4
Solving Right Triangles
Objective:
SWBAT determine the number of significant digits in a
number and solve a right triangle.
Significant Digits
According to this definition,
Significant Digits
The relationship between the accuracy of the sides of a
triangle and the accuracy of the angles in the same triangle is
shown in the table:
•
We are now ready to use the definition of significant digits to
solve right triangles. We solve a right triangle by using the
information given about it to find all of the missing sides and
angles.
Solving a Triangle
To solve a triangle means to find the measures of all the
angles and sides of the triangle.
When solving triangles, a labeled
sketch is an important aid.
Use a to represent the length of
the side opposite angle A, b for
the length of the side opposite
angle B, and so on.
In a right triangle, the letter c is reserved for the hypotenuse.
Solving Right Triangles
Unless stated otherwise, we round our answers so that the
number of significant digits in our answers matches the number
of significant digits in the least significant number given in the
original problem.
Also, we round our answers only and not any of the numbers in
the intermediate steps.
Finally, we are showing the values of the trigonometric functions
to four significant digits simply to avoid cluttering the page with
long decimal numbers.
Solving a Right Triangle Given Two Sides
In right triangle ABC, a = 2.73 and b = 3.41. Find the remaining
side and angles.
Solution:
We can find A by using the formula for tan A.
Now, to find A, we use a calculator.
Solving a Right Triangle Given Two Sides
In right triangle ABC, a = 2.73 and b = 3.41. Find the remaining
side and angles.
Solution:
Next we find B.
Use the Pythagorean Theorem to find c
Solving a Right Triangle Given Two Sides
Solve right triangle ABC if a = 11.47 cm and c = 27.82 cm.
side opposite
sin A 
hypotenuse
11.47

 .412293314
27.82
sin 1 A  24.35
• B = 90  24.35
B = 65.65
B
a = 11.47
c = 27.82
C
b2  c2  a 2
b 2  27.822  11.47 2
b  25.35
A
Solving a Right Triangle Given Two Sides
In right triangle ABC, if a = 29.43 cm and c = 53.58 cm.
Solution:
Use the Pythagorean Theorem to find b
SOLVING A RIGHT TRIANGLE GIVEN AN ANGLE & A SIDE
Solve right triangle ABC, if A = 34°30′ and c = 12.7 in.
Solving a Right Triangle, Given an Angle & a Side
Solve right triangle ABC, if A = 42 30' and c = 18.4.
• B = 90  42 30'
B
B = 47 30'
a
sin A 
c
a
sin 42 30' 
18.4
a  18.4sin 42o30'
o
c = 18.4
4230'
C
A
b
cos A 
c
a  18.4(.675590207)
b
18.4
b  18.4cos 42o30'
a  12.43
b  13.57
cos 42o30' 
Homework
• Page 73-74
# 9-14, 19 and 20