Transcript geo8-4

1. Refer to the figure. Find x and y.
2. The length of the diagonal of a square is
cm. Find
the perimeter of the square.
3. The side of an equilateral triangle measures 21 inches.
Find the length of an altitude of the triangle.
4. In the right triangle shown in the
figure, find CD if DE = 5.
• Find trigonometric ratios using right triangles.
• Solve problems using trigonometric ratios.
• trigonometry
• trigonometric ratio
• sine
• cosine
• tangent
Find Sine, Cosine, and Tangent Ratios
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
Find Sine, Cosine, and Tangent Ratios
Find Sine, Cosine, and Tangent Ratios
Find Sine, Cosine, and Tangent Ratios
Find Sine, Cosine, and Tangent Ratios
Answer:
A. Find sin A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
B. Find cos A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
C. Find tan A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
D. Find sin B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
E. Find cos B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
F. Find tan B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
Use a Calculator to Evaluate Expressions
A. Use a calculator to find tan 56° to the nearest ten
thousandth.
KEYSTROKES: TAN
56
Answer: tan 56° ≈ 1.4826
ENTER 1.482560969
Use a Calculator to Evaluate Expressions
B. Use a calculator to find cos 89° to the nearest
ten-thousandth.
KEYSTROKES: COS 89
Answer: cos 89° ≈ 0.0715
ENTER
0.071452406
A. Use a calculator to find sin 48° to the nearest ten
thousandth.
A. 0.6691
B. 1.1106
C. 0.7431
D. 0.7314
1.
2.
3.
4.
A
B
C
D
B. Use a calculator to find cos 85° to the nearest ten
thousandth.
A. 0.0872
B. 0.9962
C. 11.4301
D. 0.0698
1.
2.
3.
4.
A
B
C
D
Use Trigonometric Ratios to Find a Length
EXERCISING A fitness trainer sets the incline on a
treadmill to 7°. The walking surface is 5 feet long.
Approximately how many inches did the trainer
raise the end of the treadmill from the floor?
Let y be the height of the treadmill from the floor in
inches. The length of the treadmill is 5 feet, or 60 inches.
Use Trigonometric Ratios to Find a Length
Multiply each side by 60.
Use a calculator to find y.
KEYSTROKES: 60
SIN
7
ENTER
7.312160604
Answer: The treadmill is about 7.3 inches high.
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
the ramp is about 4.8°, how high does the ramp rise
off the ground to the nearest inch?
A. 1 in.
B. 11 in.
C. 16 in.
D. 15 in.
1.
2.
3.
4.
A
B
C
D
Use Trigonometric Ratios to Find an
Angle Measure
COORDINATE GEOMETRY Find mX in right ΔXYZ
for X(–2, 8), Y(–6, 4), and Z(–3, 1).
Use Trigonometric Ratios to Find an
Angle Measure
Explore You know the coordinates of the vertices of a
right triangle and that
is the right angle. You
need to find the measures of one of the angles.
Plan
Use the Distance Formula to find the measure
of each side. Then use one of the trigonometric
ratios to write an equation. Use the inverse to
find
Solve
or
Use Trigonometric Ratios to Find an
Angle Measure
or
or
Use Trigonometric Ratios to Find an
Angle Measure
Use the cosine ratio.
Simplify.
Solve for x.
Use Trigonometric Ratios to Find an
Angle Measure
Use a calculator to find
KEYSTROKES:
2ND
4 ÷
5 )
ENTER
Examine Use the sine ratio to check the answer.
Simplify.
Use Trigonometric Ratios to Find an
Angle Measure
KEYSTROKES:
2ND
3
÷ 5
)
ENTER
Answer: The measure of X is about 36.9.