Do Now

Rewrite as a decimal to nearest ten thousandth place (4 decimal places).

1. 13/242. 24/13Solve3. 0.3 = m/84. 1.25 = 7/y5. Find the unknown value in a right Δ if the

hypotenuse is 6.9 and one leg is 3.5.

Right-Triangle Trigonometry

Section 13.1

Essential Question

• How do I find the trigonometry functions of acute angles and solve a right triangle using trigonometry functions?

SOH CAH TOA

Example 1

Find the values of the 6 trig functions of < X for Δ XYZ. Give exact answers (fractions) and answers rounded to the nearest ten-thousandth (four decimal places).

Example 2

Find the values of the 6 trig functions of < L for ∆ KLM. Give exact answers and answers rounded to the nearest ten thousandth place (four decimal places).

Assignment

• Pg. 833, 8-31 all

Pg. 833 8-31 all

8. 8/17, 0.47069. 15/17, 0.882410. 8/17, 0.470611. 15/17, 0.882412. 8/15, 0.533313. 15/8, 1.875014. 17/15, 1.133315. 17/8, 2.125016. 17/15, 1.1333

17. 17/8, 2.125018. 8/15, 0.533319. 15/8, 1.8750

20-31 on next slide

#’s 20-31

3 1320. ,0.8321

13

2 1321. ,0.5547

13

2 1322. ,0.5547

13

3 1323. ,0.8321

13

324. ,1.52

225. ,0.66673

1326. ,1.2019

3

1327. ,1.8028

2

1328. ,1.8028

2

1329. ,1.2019

3

230. ,0.666733

31. ,1.52

Do Now:

Find all six trig functions for < Z. Give exact answers (reduced fractions) and answers rounded to the nearest ten-thousandths.

SIN= CSC= COS= SEC= TAN= COT=

X

Y Z

8

15

17

Finding angle measures

To find the measurement of an angle in a right triangle using only the lengths of two sides, you must use the inverse of the appropriate trig function.

***Your graphing calculator must be set to “degrees” in the “mode” function.

Example 3

Solve ∆ RST. Give m < R and m < S to the nearest degree, and give RT to the nearest tenth:

R

S

T

8.38.6

_________

_______

_______

RT

Sm

Rm

Example 4

For ∆ ABC find each side length to the nearest tenth and the measurement of < B:

A

B

C

414.7

_________

_________

_______

BC

AB

Bm

Example 5

For ∆ RST, find each side length to the nearest tenth and any missing angle measure:

R

S

T37

6.9

_________

_________

_______

RT

ST

Sm

Example 6

Find the length BE in the figure below:

Assignment

• Pg. 833-834, 32-43 all

Do Now

1. Solve ∆ PQR. Find the measurement of <Q to the nearest degree and RP and RQ to the nearest tenth.

2. Find the values for the six trig functions for <X for ∆ XYZ. Give exact answers and answers rounded to the nearest ten-thousandth.

P

QR

313.7

1

12

Do Now

1. Solve ∆ ABC. Find the measurement of <A to the nearest degree and AC and BC to the nearest tenth.

2. Find the values for the six trig functions for <Z for ∆ XYZ. Give exact answers and answers rounded to the nearest ten-thousandth.

Pg. 833-834, 32-43 all

32. 36°33. 30°34. 48°35. 21°36. 49°37. 41°38. < A = 39°, < B = 51°AB = 6.4

39. < R = 32°, < S = 58ST = 2.140. < A = 40°, AB = 9.5AC = 7.341. < S = 50°, RS = 11.4RT = 8.742. < B = 55°, AC=10.2BC = 7.243. < B = 48°, BC = 3.8AC = 4.2

QUIZ TOMORROW OVER 13.1!!

Today’s Assignment: • pg. 982 13.1, 13-18 all• Worksheet 13.1, 1-15 all

Pg. 982, 13.1 #’s 1-18

1. 20/29, 0.68972. 21/29, 0.72413. 21/29, 0.72414. 20/29, 0.68975. 20/21, 0.95246. 21/20, 1.057. 29/20, 1.458. 29/21, 1.38109. 29/21, 1.381010. 29/20, 1.45

11. 21/20, 1.0512. 20/21, 0.952413. <G=53°, GI=2.6,

GH=4.414. <E=52°, <D=38°,

EF=4.315. <J=56°, <K=34°,

JK=14.416. <A=27°, <B=63°,

AB=6.7

Continued…

17. <M=64°, MN=22.1, NO=19.9

18. <R=32°, SQ=8.1, QR=13.0

Workbook pg.82,13.11. 40/41, 0.97562. 9/41, 0.21953. 40/9, 4.44444. 9/41, 0.21955. 40/41, 0.9756

6. 9/40, 0.2257. 41/9, 4.55568. 41/9, 4.55569. 40/9, 4.444410. XZ=8.3, <X=57°,

<Z=33°11. UV=11.6, <U=61°,

<W=29°12. RT=21.6, <R=34°,

<T=56°

Continued…

13. <Q=59°, QN=4.9, NP=4.2

14. <L=36°, LM=4.9, MN=3.5

15. <J=56°, HJ=5.2, HK=4.3