1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles. 2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles. 3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.

1. I can label the sides of a right triangle.
I can set up the trig ratios.
I can use the trig ratios to solve for the missing
side length & angle measures of a right
triangle.

2. H
AT
15
9
Calculate the length of
hypotenuse
leg
leg
?
Use the Pythagorean theorem
-81 -81
x = 12

3. H
AT
15
9
hypotenuse
Opp. leg
Adj.
leg
12
Set up the following trig ratios
Sin H =
Cos H =
Tan H =
Sin A =
Cos A =
Tan A =
Adj.
leg
Opp. leg

4. H
C
Calculate the length of
hypotenuse
legleg
?
Use the Pythagorean theorem
x = 6

5. hypotenuse
Set up the following trig ratios
H
C
6
Sin S =
Cos S =
Tan S =
Sin H =
Cos H =
Tan H =
Adj.
leg
Opp.
leg

6. If Sin A = , find the Cos A.
*Draw a triangle and label.
A
Opp.leg
Adj. leg
6
8
x
-36 -36
Cos A =

7. Use the last example as a model problem to
complete the following:
1. If Tan A = , find Sin B.
2. If Cos B = , find Tan A.

8. Solving Right Triangles means to calculate
missing side lengths and angle measures of a
right triangle.
When evaluating sine, cosine, or tangent you need
to make sure your calculator is in degree mode.
MODE Radian Degree

9. Evaluating Angles in the calculator.
(A) Sin 52
o
(B) Cos 122
o
(C) Tan 45
o
(D) Sin 0
o
(E) Cos 90
o
(F)Tan 90
o

10. A
B
C
x y
250
37
o
Solve for x and y
Why can’t you use the
Pythagorean Theorem?Opp. leg
Adj. leg
Which side should be the longest? Why?

11. Solve for x and y
A
B
C
x
y 10
61
o
Opp. leg
Adj. leg

12. Solve for x and y
A
B
C
x
13
34
o
Opp. leg
Adj. leg

13. Using the inverse function to solve for angles
Notice if you use the 2nd button and then choose a trig
function, you are using the inverse.
Sin-1 Cos-1 Tan-1
(a) (b)Sin-1 Sin-1 Cos-1 Cos-1

14. Use the examples on the previous slide as model problems to
help complete the following problems.
(c) (d)
(e) (f)
Sin-1
Sin-1

15. Find the measures of the acute angles in a right
triangle.
*Remember: the 2 acute angles of a right triangle are
complementary
FIND: m<A and m<B
A
B
C
11.2
Opp. leg
Adj. leg
9.8 + 80.2 = 90

16. A
BC 10.8
24.7
Find the m<A and m<B

17. A
BC
72
Find the m<A and m<B