Essential Question: How do we use trigonometric functions to find the missing imformation of right triangles?
Learning Target: Students will be able to construct trigonometric ratios to solve real world problems involving right triangles.
Show your work and use complete sentences for credit.
Day 1 4/9/25
Review: Right Triangle Proportions
Required
2
Question 1
1.
Which length completes the proportion?
_______
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2
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10
G.SRT.5
Review: Pythagorean Formula
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2
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5
Required
10
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5
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10
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10
Creating Trigonometric Ratios
Required
6
Required
30
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30
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30
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30
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30
Day 2 4/10/25
Required
24
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24
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24
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
Question 38
38.
A support wire is attached to the top of a 20 m tall observation tower. If the support wire and the ground form an angle of 46 degrees, what is the length of the support wire, to the nearest tenth?
Question 39
39.
At a point 30 feet from the base of a tree, the angle formed with the ground looking to the top measures 53 degrees. Find, to the nearest foot, the height of the tree. (Make sure to draw a diagram to help you solve the problem)
Question 40
40.
The angle of elevation of the top of a flagpole from a point on the ground 30 meters from the base of the flagpole is 18 degrees. What is the height of the flagpole, to the nearest meter? (Make sure to draw a diagram to help you solve the problem)
Question 2
2.
Which length completes the proportion?
_______
Question 3
3.
Error Analysis: A classmate wrote an incorrect proportion to find x. Explain and correct the error.
Question 4
4.
Review: The Pythagorean Theorem works for which triangle(s)?
Question 5
5.
The hypotenuse is the _______ side of a right triangle.
Question 6
6.
Review: Prove that the measurements 6 ft, 8 ft, and 10 ft make a right triangle.
Question 7
7.
Review:
Solve the equation.
w=_______
Question 8
8.
Review: Find the missing side of the right triangle.
a= 24
b=10
c=_______
Question 9
9.
Review: Find the missing side of the right triangle.
a = 8
b=_______
c = 10
Question 10
10.
Complete the three trigonometric ratios:
Sine is ratio of _____________
_______________
Cosine is ratio of _____________
_______________
Tangent is ratio of _____________
_____________
Other Answer Choices:
adjacent
opposite
hypotenuse
Question 11
11.
Find the value of each trigonometric ratio
sin A=_______
cos A=_______
tan A=_______
sin C=_______
cos C=_______
tan C=_______
Question 12
12.
Find the value of each trigonometric ratio
sin A=_______
cos A=_______
tan A=_______
sin C=_______
cos C=_______
tan C=_______
Question 13
13.
Find the value of each trigonometric ratio
sin X=_______
cos X=_______
tan X=_______
sin Z=_______
cos Z=_______
tan Z=_______
Question 14
14.
Find the length of the missing side
QR=_______
Find the value of each trigonometric ratio
sin R=_______
cos R=_______
tan R=_______
sin P=_______
cos P=_______
tan P=_______
Question 15
15.
Find the length of the missing side.
ST=_______
Find the value of each trigonometric ratio
sin R=_______
cos R=_______
tan R=_______
sin S=_______
cos S=_______
tan S=_______
Finding Missing Side Lengths Using Trigonometry
This how you use the Desmos Scientific calculator to simplify trig expressions
Question 16
16.
Use desmos to calculate the following trigonometric functions (be sure to round your answer to the nearest tenth):
cos 30=_______
sin 30=_______
tan 30=_______
sin 67=_______
cos 53=_______
tan 45=_______
Question 17
17.
Use desmos to calculate the following trigonometric functions (be sure to round your answer to the nearest tenth):
12 cos 30=_______
6 sin 30=_______
7 tan 30=_______
Question 18
18.
Use desmos to evaluate the following trigonometric functions (be sure to round your answer to the nearest tenth):
a)_______
b)_______
c)_______
d)_______
Question 19
19.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 20
20.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 21
21.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 22
22.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 23
23.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 24
24.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 25
25.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 26
26.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 27
27.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 28
28.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Question 29
29.
What trigonometric function could you use to solve for x? (sin, cos, or tan)
_______
What is the length of x? (Round your answer to nearest tenth)
_______
Using Trigonometry to Find Missing Angles
Question 30
30.
Evaluate these inverse trigonometric functions (Round your answer to nearest tenth):
sin⁻¹(3/5)=_______
cos⁻¹(8/17)=_______
tan⁻¹(3/4)=_______
sin⁻¹(9/41)=_______
tan⁻¹(4/9)=_______
cos⁻¹(22/36)=_______
Question 31
31.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 32
32.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 33
33.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 34
34.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 35
35.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 36
36.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)
m∠θ=_______°
Question 37
37.
What inverse trigonometric function could you use to find the missing angle? (sin⁻¹, cos⁻¹, or tan⁻¹)
_______
What is the measure of θ ? (Round your answer to nearest degree)