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Name ________________________________________ Date __________________ Class __________________
LESSON
13-1
Tangent Ratio
Practice and Problem Solving: A/B
Identify the relationships in the figure to the right.
1. tanX =
3. tan−1
WX
=
VW
= m∠_____
WX
5. tanX × tanV = _____
2. tanV =
4. tan−1
WX
= m∠_____
VW
6. tan−1 VW + tan−1 WX = _____°
WX
VW
Use a calculator to find each tangent or inverse tangent. Round
tangents to the nearest 0.01 and angles to the nearest 0.1 degree.
Check the inverse tangents by finding the tangent of each angle.
7. tan23° ≈ _____________
10. tan−10.14 ≈ _____________°
tan _____________° ≈ 0.14
8. tan43° ≈ _____________
11. tan−11= _____________°
9. tan47° ≈ _____________
12. tan−16.1 ≈ _____________°
tan _____________° = 1
tan _____________° ≈ 6.1
Solve Problems 13–16 using tangent ratios and a calculator. Refer to
the figure to the right of each problem.
13. To the nearest hundredth, what is tanM in
+LMN ? ________
14. Write a ratio that gives tanS. ________ Find the value of tanS to
the nearest hundredth. ________ Use the inverse tangent function
on your calculator to find the angle with that tangent. ________
15. Write and solve a tangent equation to find the distance from
C to E to the nearest 0.1 meter. ________ meters
16. The glide slope is the path a plane uses while it is landing
on a runway. The glide slope usually makes a 3° angle with
the ground. A plane is on the glide slope and is 1 mile (5280 feet)
from touchdown. Find EF, the plane’s altitude, to the
nearest foot. Show your work.
_________________________________________________________________________________________
_________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
253
Name ________________________________________ Date __________________ Class __________________
LESSON
13-2
Sine and Cosine Ratios
Practice and Problem Solving: A/B
After verifying that the triangle to the right is a right triangle,
use a calculator to find the given measures. Give ratios to the
nearest hundredth and angles to the nearest degree.
1. Use the Pythagorean Theorem to confirm that the triangle
is a right triangle. Show your work.
________________________________________________________________
2. sin∠1 =
≈ _________________
3. sin∠2 =
4. cos∠1 =
= _________________
5. cos∠2 =
= _______________________
≈ _______________________
6. Show how to find m∠1 using the inverse sine of ∠1.
_________________________________________________________________________________________
7. Show how to find m∠2 using the inverse sine of ∠2.
_________________________________________________________________________________________
Use a calculator and trigonometric ratios to find each length.
Round to the nearest hundredth.
8.
9.
BD = _________________
10.
QP = _________________
ST = _________________
Use sine and cosine ratios to solve Problems 11–13.
11. Find the perimeter of the triangle. Round to the nearest
0.1 centimeter. _________________
12. To the nearest 0.1 inch, what is the length of the hypotenuse
of the springboard shown to the right? _________________
13. What is the height of the springboard (the dotted
line)? _________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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