Check point 7.3-7.4
7.3 P 453-4
#4 #16
7.4 P 461
#4
# 8
Geometry
Section 7.5 & 7.6
I can find the sin, cos, and tan ratios given the side of a right triangle.
SOH CAH TOA
Sine, Cosine, Tangent Ratios
EXAMPLE 1 Find sine ratios
Find sin S and sin R. Write each answer as a fraction and as a decimal rounded to four places.
SOLUTION
sin S = opp. Shyp
= RTSR = 63
65 0.9692
sin R = opp. Rhyp
= STSR = 16
65 0.2462
EXAMPLE 2 Find cosine ratios
Find cos S and cos R. Write each answer as a fraction and as a decimal rounded to four places.
SOLUTION
cos S = adj. Shyp
= STSR = 16
65 0.2462
cos R = adj. Rhyp
= RTSR = 63
65 0.9692
EXAMPLE 1 Find tangent ratios
Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.
SOLUTION
tan S =opp S
adj S= RTST
= 80 18
= 40 9
4.4444
tan R =opp R
adj R= STRT
= 18 80
= 9 40
0.2250=
EXAMPLE 6 Use a special right triangle to find a sine and cosine
Use a special right triangle to find the sine and cosine of a 60o angle.
SOLUTION
Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 60o angle.
3
sin 60o =opp. hyp.
=3
20.08660
cos 60o =adj. hyp.
=21
0.5000=
2. Find the values of x (find the missing leg) and y (find the hypotenuse).
yy
Solutions for Check point 7.3-7.4
7.3 P 453
#4 #16
7.4 P 461
#4
# 8
∆KML ~ ∆MNL ~ ∆KNM
L
K
M
MN
L
KMN x
x
x
x
6
36
9
4
2
10
25
225
2
hyp
hyp
hyp
leghyp
18
92
2
y
y
legshorthyp
39
3
x
legshortleglong
WARM UP: Lesson 7.6, For use with pages 473-480
2. Name the leg opposite X.
Use this diagram for Exercises 1-4.
1. Name the hypotenuse.
ANSWER YZ
ANSWER XZ
3. Name the leg adjacent to X.
ANSWER XY
Check point 7.4 -7.5-6
7.4
7.5-6
1) Draw and Label the sides on a 45° – 45° – 90° Triangle
2) Draw and Label the sides on a 30° – 60° – 90° Triangle
4) List the trigonometric ratios for sine, cosine, and tangent
3) Draw and label the sides of the right triangle with respect to A.
Hint: Opposite, Adjacent, Hypotenuse
A
C B
Geometry
Section 7.5 & 7.6 Combined
(I can draw a picture and solve a story problem using sin, cos, and tan)
1. Find sin J , cos K, tan K. Round to four decimal places.
EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse
DOG RUN
You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.
55
EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse
SOLUTION
sin 35o =opp hyp Write ratio for sine of 35o.
sin 35o = 11x
Substitute.
x sin 35o = 11 Multiply each side by x.
x = 11. sin 35o Divide each side by tan. 35o
x 11. 0.5736
Use a calculator to find tan. 35o
x 19.2 Simplify.
ANSWER
You will need a little more than 19 feet of cable.
EXAMPLE 4 Find a hypotenuse using an angle of depression
SKIING
You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain?
EXAMPLE 4 Find a hypotenuse using an angle of depression
SOLUTION
sin 21oWrite ratio for sine of 21o.
sin 21o Substitute.
x sin 21o = 1200 Multiply each side by x.
x = 1200. sin 21o Divide each side by sin 21o
x 1200. 0.3584
Use a calculator to find sin 21o
x 3348.2 Simplify.
opp hyp=
1200x=
ANSWER
You ski about 3348 meters down the mountain.
A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?
Launch
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