Transcript Solving Right Triangles - Effingham County Schools

MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
1. Use the quadratic formula to solve the equation x2 + 5x - 1 = 0.
A.
5  21
x
2
5  29
B. x 
2
C. x 
5  29
5  21
D. x 
2
2
D.
2. Factor: 4x2 – 49
A.
(2x + 7)(2x - 7)
B.
(2x – 7)(2x - 7)
C.
D.
(4x – 7)(x + 7)
(4x + 7)(x – 7)
A.
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
How do you solve right triangles?
Day 54
Lesson 5.4
Wednesday, April 6, 2016
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
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.
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
1. Solve the right triangle. Round to the nearest tenth.
mQ  53
mR  90
mP  37°
PQ  30
PR  24.0
QR
cos53 
30
QR  18.1
sin53 
PR
30
QR  18.1
PR  24.0
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
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,
RT2 = RS2 + ST2
(5.7)2 = 52 + ST2
Since the acute angles of a right
triangle are complementary,
mT  90° – 29°  61°.
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
3. Solve the right triangle. Round decimals
the nearest tenth.
Use Pythagorean Theorem to find AB.
AB 2  22  32
AB  3.6
Use an inverse trig function to
find a missing acute angle…
3
mA  tan ( )  56.3
2
1
Use Triangle Sum Theorem to
find the other acute angle…
mB  90  56.3  33.7
AB  3.6
BC  3
AC  2
mA  56.3°
mB  33.7°
mC  90
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
tan 55o 
55o
555
g
g  388.6 ft.
555
555 ft
55o
g
55o
g
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
PN 2  112  18 2
PN  21.1
11
mN  tan ( )  31.4
18
1
mP  90  31.4  58.6
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
232  TU 2  72
TU  21.9
7
mS  cos ( )  72.3
23
1
mU  90  72.3  17.7
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
 Assignment:
◦ Pg 174 (#7 – 14.)
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.
MM2G2
Students will define and apply sine, cosine, and tangent ratio to right triangles.
Ladder Problems
http://www.geogebra.org/en/examples/ladder_wall/ladder_wall.html
MM2G2b Explain the relationship of the trigonometric ratios of complementary angles.
MM2G2c Solve application problems using the trigonometric ratios.