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8-4 Trigonometry, day 2
You used the Pythagorean Theorem to find missing
lengths in right triangles.
• Find trigonometric ratios using right
triangles.
• Use trigonometric ratios to find angle
measures in right triangles.
You can use a calculator to find the measure of an
angle which is the inverse of the trigonometric ratio
(sine, cosine, or tangent of an acute angle).
p. 571
Inverse Trigonometric Ratios
The expression 𝑠𝑖𝑛−1 𝑥 is read the inverse
sine of x and is interpreted as the angle with
sine x.
Use the thought:
If the tan 30°≈.058, then tan−1 0.58 ≈ 30°
Use a calculator to find the
measure of P to the
nearest tenth.
The measures given are those of the
leg adjacent to P and the
hypotenuse, so write the equation
using the cosine ratio.
KEYSTROKES: 2nd [COS] ( 13 ÷ 19 )
Answer:
ENTER
46.82644889
So, the measure of P is approximately 46.8°.
Use a calculator to find the measure of D to the
nearest tenth.
A. 44.1°
B. 48.3°
C. 55.4°
D. 57.2°
Solve the right triangle. Round
side measures to the nearest
hundredth and angle measures
to the nearest degree.
Step 1
Find mA by using a tangent ratio.
Definition of inverse
tangent
29.7448813 ≈ mA
Use a calculator.
So, the measure of A is about 30.
Step 2 Find mB using
complementary angles.
mA + mB =90
30 + mB ≈ 90
mB ≈ 60
Definition of
complementary
angles
mA ≈ 30
Subtract 30 from
each side.
So, the measure of B is about 60.
Step 3
Find AB by using the Pythagorean Theorem.
(AC)2 + (BC)2 = (AB)2
Pythagorean Theorem
72 + 42
= (AB)2
Substitution
65
= (AB)2
Simplify.
Take the positive
square root of each
side.
8.06
≈ AB
Use a calculator.
So, the measure of AB is about 8.06.
Answer:
mA ≈ 30, mB ≈ 60, AB ≈ 8.06
Solve the right triangle. Round side measures to
the nearest tenth and angle measures to the
nearest degree.
A. mA = 36°, mB = 54°,
AB = 13.6
B. mA = 54°, mB = 36°,
AB = 13.6
C. mA = 36°, mB = 54°,
AB = 16.3
D. mA = 54°, mB = 36°,
AB = 16.3
8-4 Assignment day 2
Page 573, 12-15,
36-39, 42-44