MM2G2 Students will define and apply sine, cosine, and tangent ratio to right triangles. MM2G2b Explain the relationship of the trigonometric ratios of

MM2G2 Students will define and apply sine, cosine, and tangent ratio to right triangles.

MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.MM2G2c Solve application problems using the trigonometric ratios.

1. Use the quadratic formula to solve the equation x2 + 5x - 1 = 0.

5 21

2

x 5 29

2

x

5 21

2

x

5 29

2

xA. B. C. D.

D.

2. Factor: 4x2 – 49A. (2x + 7)(2x - 7) C. (4x – 7)(x + 7)B. (2x – 7)(2x - 7) D. (4x + 7)(x – 7)

A.



How do you solve right triangles?

Tuesday, April 18, 2023

Lesson 5.4

Day 54



Every right triangle has one right angle, two acute angles, one hypotenuse, and two legs.

To SOLVE A RIGHT TRIANGLE means to find all 6 parts.



1. Solve the right triangle. Round to the nearest tenth.

53

90

30

m Q

m R

m P

PQ

PR

QR

cos53

30

QR sin5330

PR

37°

18.1

24.0

18.1QR 24.0PR



Solving Right Triangles

2. Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

By the Pythagorean Theorem,

Since the acute angles of a right triangle are complementary, mT 90° – 29° 61°.

RT2 = RS2 + ST2

(5.7)2 = 52 + ST2



3. Solve the right triangle. Round decimals the nearest tenth.

3

2

90

AB

BC

AC

m A

m B

m C

Use Pythagorean Theorem to find AB.

2 2 22 3

3.6

AB

AB3.6Use an inverse trig function to

find a missing acute angle…

1 3tan ( ) 56.3

2m A

Use Triangle Sum Theorem to find the other acute angle…

90 56.3 33.7m B

56.3°

33.7°



55o

555 ft

g

55o

555

g

555tan 55o

g

388.6 ft.g

55o



2 2 211 18

21.1

PN

PN

1 11tan ( ) 31.4

18m N

90 31.4 58.6m P



2 2 223 7

21.9

TU

TU

1 7cos ( ) 72.3

23m S

90 72.3 17.7m U



Assignment:◦Pg 174 (#7 – 14.)



http://www.geogebra.org/en/examples/ladder_wall/ladder_wall.html

Ladder Problems

Documents

MM2G2 Students will define and apply sine, cosine, and tangent ratio to right triangles. MM2G2b Explain the relationship of the trigonometric ratios of