Name: Date:
Student Exploration: Sine, Cosine, and Tangent Ratios
Get the Gizmo ready:
Activity A: On the SINE tab, set mA to 30°.
Sine Check that Show side lengths is turned on.
Drag point C as far as possible to the right.
1. In ΔABC, BC is the opposite leg because it is opposite A.
A. What are the lengths of each side? AC = BC = AB =
B. When mA = 30°, what is the ratio of BC to AB?
C. Drag point C to the left. Notice that mA stays the same, so the new triangle is
BC
similar to the original. For two different positions of point C, record BC, AB, and
AB
.
Position 1 Position 2
BC BC
BC AB BC AB
AB AB
What do you notice?
2. Drag point C all the way to the right so that the length of the hypotenuse AB is 14. Turn on
Show sine computation. The sine of angle A (or “sin A”) is the ratio of the opposite leg to
opposite
the hypotenuse: sin A = hypotenuse .
A. What is sin 30°?
B. Turn off Show sine computation. Set mA to 20°. What is sin 20°?
Check your work by turning on Show sine computation.
3. Turn off Show sine computation. Set mA to each of the following angles, and use the
side lengths and a calculator to find the sine of each angle. Use the Gizmo to check.
sin 15° = sin 45° = sin 60° = sin 75° =
This study source was downloaded by 100000839632511 from CourseHero.com on 03-06-2022 22:17:05 GMT -06:00
https://www.coursehero.com/file/36903718/trig-gizmodoc/
, 4. In ΔDEF, F is a right angle. Suppose mD = 12° and EF = 1.3. Find the length of the
hypotenuse, DE .
5. Lars rides a chairlift to the top of a mountain. The
chairlift rises at a constant angle of 37°. If the length
of the chairlift ride is 1,392 m, what is the elevation
gain from the base of the chairlift to the top?
Draw a right triangle to model this problem and use
the Gizmo to find sin 37°. Show your work.
Elevation gain:
This study source was downloaded by 100000839632511 from CourseHero.com on 03-06-2022 22:17:05 GMT -06:00
https://www.coursehero.com/file/36903718/trig-gizmodoc/
Student Exploration: Sine, Cosine, and Tangent Ratios
Get the Gizmo ready:
Activity A: On the SINE tab, set mA to 30°.
Sine Check that Show side lengths is turned on.
Drag point C as far as possible to the right.
1. In ΔABC, BC is the opposite leg because it is opposite A.
A. What are the lengths of each side? AC = BC = AB =
B. When mA = 30°, what is the ratio of BC to AB?
C. Drag point C to the left. Notice that mA stays the same, so the new triangle is
BC
similar to the original. For two different positions of point C, record BC, AB, and
AB
.
Position 1 Position 2
BC BC
BC AB BC AB
AB AB
What do you notice?
2. Drag point C all the way to the right so that the length of the hypotenuse AB is 14. Turn on
Show sine computation. The sine of angle A (or “sin A”) is the ratio of the opposite leg to
opposite
the hypotenuse: sin A = hypotenuse .
A. What is sin 30°?
B. Turn off Show sine computation. Set mA to 20°. What is sin 20°?
Check your work by turning on Show sine computation.
3. Turn off Show sine computation. Set mA to each of the following angles, and use the
side lengths and a calculator to find the sine of each angle. Use the Gizmo to check.
sin 15° = sin 45° = sin 60° = sin 75° =
This study source was downloaded by 100000839632511 from CourseHero.com on 03-06-2022 22:17:05 GMT -06:00
https://www.coursehero.com/file/36903718/trig-gizmodoc/
, 4. In ΔDEF, F is a right angle. Suppose mD = 12° and EF = 1.3. Find the length of the
hypotenuse, DE .
5. Lars rides a chairlift to the top of a mountain. The
chairlift rises at a constant angle of 37°. If the length
of the chairlift ride is 1,392 m, what is the elevation
gain from the base of the chairlift to the top?
Draw a right triangle to model this problem and use
the Gizmo to find sin 37°. Show your work.
Elevation gain:
This study source was downloaded by 100000839632511 from CourseHero.com on 03-06-2022 22:17:05 GMT -06:00
https://www.coursehero.com/file/36903718/trig-gizmodoc/
