8-4 trigonometry, day 2
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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. - PowerPoint PPT PresentationTRANSCRIPT
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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.
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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
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The expression is read the inverse sine of x and is interpreted as the angle with sine x.Use the thought:If the 30°≈.058, then
Inverse Trigonometric Ratios
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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: [COS] 13 1946.82644889
2nd ( ÷ ) ENTER
Answer: So, the measure of P is approximately 46.8°.
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A. 44.1°
B. 48.3°
C. 55.4°
D. 57.2°
Use a calculator to find the measure of D to the nearest tenth.
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Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree.
Step 1 Find mA by using a tangent ratio.
29.7448813 ≈ mA Use a calculator.
So, the measure of A is about 30.
Definition of inverse
tangent
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Step 2 Find mB using complementary angles.
mB ≈ 60 Subtract 30 fromeach side.
So, the measure of B is about 60.
30 + mB ≈ 90 mA ≈ 30
mA + mB =90 Definition ofcomplementaryangles
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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 positivesquare root of eachside.
8.06 ≈ AB Use a calculator.
Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06
So, the measure of AB is about 8.06.
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A. mA = 36°, mB = 54°, AB = 13.6
B. mA = 54°, mB = 36°, AB = 13.6
C. mA = 36°, mB = 54°, AB = 16.3
D. mA = 54°, mB = 36°, AB = 16.3
Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.
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8-4 Assignment day 2
Page 573, 12-15, 36-39, 42-44