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Laabri

7.8 Solving Trigonometric Functions (Due 4/15/25)

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Essential Question: How do we use trigonometric functions to find the missing information of right triangles?

Learning Target: Students will be able to construct trigonometric ratios to solve real world problems involving right triangles.

Complete the entire document and use full sentences when prompted for full credit.

Responses without work will receive no points.

Remember to upload work from paper when prompted to receive credit.

Day 1 5/4/26

Day 2 5/5/26

Review: Right Triangle Proportions

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1.

Which length completes the proportion?

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2.

Which length completes the proportion?

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3.

G.SRT.5

Review: Pythagorean Formula

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5.

The hypotenuse is the side of a right triangle.

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Using Pythagorean Theorem to Find Missing Lengths

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10.

Use the Pythagorean Theorem to find x. Round your answer to the nearest tenth.

x=

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11.

Use the Pythagorean Theorem to find x. Round your answer to the nearest tenth.

x=

Trigonometric Functions

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Creating Trigonometric Ratios

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Completing the Triangles

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Error Analysis: A classmate wrote an incorrect proportion to find x. Explain and correct the error.

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4.

Review: The Pythagorean Theorem works for which triangle(s)?

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6.

Review: Prove that the measurements 6 ft, 8 ft, and 10 ft make a right triangle.

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7.

Review:

Solve the equation.

w=

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8.

Review: Find the missing side of the right triangle.

a= 24

b=10

c=

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9.

Review: Find the missing side of the right triangle.

a = 8

b=

c = 10

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12.

Using a triangle, draw an example of a sine ratio.

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13.

Using a triangle, draw an example of a cosine ratio.

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14.

Using a triangle, draw an example of a tangent ratio.

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15.

Find the 3 trigonometric function for θ. Give each trig ratio as a fraction in simplest form.

sin θ=

cos θ=

tan θ=

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16.

Find the 3 trigonometric function for θ. Give each trig ratio as a fraction in simplest form.

sin θ=

cos θ=

tan θ=

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17.

Find the 3 trigonometric function for θ, Give each trig ratio as a fraction in simplest form. (This mean is fraction form.)

sin θ=

cos θ=

tan θ=

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18.

Give each trig ratio as a fraction in simplest form.

Sin Q

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19.

Give each trig ratio as a fraction in simplest form.

Cos Q

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20.

Give each trig ratio as a fraction in simplest form.

Tan Q

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21.

Give each trig ratio as a fraction in simplest form.

sin R

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22.

Give each trig ratio as a fraction in simplest form.

Cos R

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23.

Give each trig ratio as a fraction in simplest form.

Tan R

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24.

Complete the three trigonometric ratios:

Mmuae Afoforo a Wobɛpaw:
hypothenuse
adjacent
opposite
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25.

Find the value of each trigonometric ratio

sin A=

cos A=

tan A=

sin C=

cos C=

tan C=

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26.

Find the value of each trigonometric ratio

sin A=

cos A=

tan A=

sin C=

cos C=

tan C=

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27.

Find the value of each trigonometric ratio

sin X=

cos X=

tan X=

sin Z=

cos Z=

tan Z=

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28.

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=

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29.

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=

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30.

What is cos 65? (Round your answer to 2 decimal places.)

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31.

What is tan 48? (Round your answer to 2 decimal places.)

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32.

What is sin 32? (Round your answer to 2 decimal places.)

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33.

Solve for x. Round to the nearest tenth.

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34.

Solve for x. Round to the nearest tenth.

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35.

Solve for x. Round to the nearest tenth.

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36.

Solve for x. Round to the nearest tenth.

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37.

Solve for x. Round to the nearest tenth.

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38.

Solve for x. Round to the nearest tenth.

More "Completing the Triangle"

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39.

Use the Pythagorean theorem to solve for x. Round your answer to the nearest tenth.

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40.

Use the Pythagorean theorem to solve for x. Round your answer to the nearest tenth.

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41.

Find the missing side. Round your answer to the nearest tenth.

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42.

Solve for x. Round your answer to the nearest tenth.

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43.

Solve for x. Round your answer to the nearest tenth.

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44.

Solve for x. Round to the nearest hundredth.

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45.

Find KL. Round to the nearest hundredth.

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46.

A wire is attached from the top of a 30-foot tall telephone pole to a stake in the ground.

If the angle formed by the wire and the pole is 48°, what is the length of the wire? Round your answer to the nearest hundredth.