Download Special Right Triangles Practice Set C

Develop an understanding of and apply special right triangle rules to find
missing side lengths of right triangles, Practice Set C
Name:
Date:
1. Use your calculator to find the following values to four decimal places:
tan 45˚ ________________ sin 45˚ ________________ cos 45˚ ________________
a. Fill in the chart below based on the figure above. Round decimal answers to the
nearest ten thousandths. Follow the example in the first row of the chart.
a
3
b
c
3
tan
ratio as
sin
ratio as
cos
ratio as
ratio
decimal
ratio
decimal
ratio
decimal
1
4
8
9
b. What do you notice?
.7071
.7071
c. Why do you think the ratio for each trigonometric function stays the same even
when the side length changes?
2. Use your calculator to find the following values to four decimal places:
tan 30˚ ________________ sin 30˚ ________________ cos 30˚ ________________
tan 60˚ ________________ sin 60˚ ________________ cos 60˚ ________________
a. Fill in the chart below based on the figure above. Round decimal answers to the
nearest ten thousandths. Follow the example in the first row of the chart.
a
b
3
c
6
8
9
10
b. What do you notice?
tan
ratio as
sin
ratio as
cos
ratio as
ratio
decimal
ratio
decimal
ratio
decimal
.5774
.5
.8660
c. Why do you think the ratio for each trigonometric function stays the same even
when the side length changes?
d. Why do you think these two triangle types are called special? Might there be any
other triangles that should be called special?
Develop an understanding of and apply special right triangle rules to find
missing side lengths of right triangles, Practice Set C
Answer Key
1. Use your calculator to find the following values to four decimal places:
tan 45˚ ____1___________ sin 45˚ ____.7071_______ cos 45˚ ____.7071________
a. Fill in the chart below based on the figure above. Round decimal answers to the
nearest ten thousandths. Follow the example in the first row of the chart.
a
b
3
3
4
4
c
tan
ratio as
sin
ratio as
cos
ratio as
ratio
decimal
ratio
decimal
ratio
decimal
1
4sqrt 2
4/4
1
.7071
4/4sqrt
.7071
2
5
5
5/5
1
5/5sqrt
4sqrt2
8
4sqrt2/
1
4sqrt2
9sqrt2
9sqrt2/
/2
2
9
b. What do you notice?
9sqrt2/
9sqrt2
4sqrt2/
.7071
sqrt2/2
.7071
5/5sqr
.7071
t2
.7071
8
1
4/4sqr
t2
2
4sqrt2
.7071
4sqrt2
.7071
/8
.7071
sqrt2/
2
.7071
Answers may vary. The purpose of this question is for students to begin to see how
the angle measure and the sides relate to each other. So student answers need to
go beyond the same value appears.
c. Why do you think the ratio for each trigonometric function stays the same even
when the side length changes?
Answers may vary. The purpose of this question is for students to begin to
understand that all 45-45-90 triangles are similar. This idea is continued in the next
lesson
2. Use your calculator to find the following values to four decimal places:
tan 30˚ ____.5774_______ sin 30˚ _____.5__________ cos 30˚ ____.8660______
tan 60˚ ____1.7321______ sin 60˚ ______.8660______ cos 60˚ _____.5_________
a. Fill in the chart below based on the figure above. Round decimal answers to the
nearest ten thousandths. Follow the example in the first row of the chart.
a
b
3
4
c
tan
ratio as
sin
ratio as
cos
ratio as
ratio
decimal
ratio
decimal
ratio
decimal
6
4sqrt3
8
.5774
4/4sqrt
3
.5774
.5
4/8
.5
.8660
4sqrt3
/8
.8660
5
10
5/5sqrt
.5774
5/10
.5
3
3sqrt3
9
6sqrt3
3sqrt3/
10
3/3
20sqrt
sqrt3/3
.8660
/10
.5774
9
10sqrt
5sqrt3
3sqrt3/
.5
6sqrt3
.5774
3/3
sqrt3/2
sqrt3
9/6sqr
.8660
t3
.5
10/20
.8660
sqrt3
b. What do you notice?
Answers may vary.
c. Why do you think the ratio for each trigonometric function stays the same even
when the side length changes?
Answers may vary.
d. Why do you think these two triangle types are called special? Might there be any
other triangles that should be called special?
Answers may vary. The goal of this questions is to solidify the notion that these two
types of right triangles have side lengths that create ratios with values that we can
easily compute.