1. Copyright © 2014 Pearson Education, Inc.10
CHAPTER
10.2 Tangent Ratio
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2. Copyright © 2014 Pearson Education, Inc.
Trigonometric Ratios
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3. Writing Trigonometric Ratios
What is the tangent ratio for ∠T? Solution The opposite value and the adjacent value depend on the angle. We are interested in ∠T, so opposite ∠T is 8 units and the leg adjacent to ∠T is 15 units.
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4. Writing Trigonometric Ratios for 45°
Find the tangent of 45°. Give an exact value and a four-decimal place approximation. Solution Since the legs are the same length, choose one of the two 45° angles.
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5. Writing Trigonometric Ratios for 45°
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6. Finding the Distance Across a Lake
To find the distance across a lake, a surveyor took the measurements shown in the figure. Use these measurements to determine how far it is across the lake. Round to the nearest yard. Solution We do have an angle of 40°. The unknown value is opposite the 40° angle, and 630 yd is adjacent to the 40° angle. The trigonometric function having to do with opposite and adjacent is tangent.
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7. Finding the Distance Across a Lake
The distance across the lake is approximately 529 yards.
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8. Copyright © 2014 Pearson Education, Inc.
Trigonometric Ratios
If we know the sine, cosine, or tangent ratio for an angle, we can use an inverse (sin-1, cos-1, or tan-1) to find the measure of the angle.
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9. Using Inverses to Find Angle Measures
a. What is m∠X to the nearest degree?
Solution
We know the lengths of the hypotenuse and the side opposite ∠X. We use the sine ratio. 10
Enter
Sin-1 6 ÷
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10. Using Inverses to Find Angle Measures
b. What is m∠X to the nearest degree?
Solution
We know the lengths of the hypotenuse and the side adjacent ∠X. We use the cosine ratio. 15 20
Enter
Cos-1 ÷
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