Podcast
Questions and Answers
In ∠ DEF, which of the following angles is the vertex angle?
What best describes the angles ∠X and ∠Y if ∠X = 95⁰ and ∠Y = 85⁰?
supplementary
If ∠A and ∠B are complementary angles and ∠A = 42⁰, how many degrees is ∠B?
48⁰
Which of the following describes ∠C if ∠C = 120⁰?
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In triangle ABC, if ∠A = 40⁰ and ∠B = 80⁰, what is the value of ∠C?
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Which conversion factor is used to convert degrees into radians?
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Find the other acute angle of a right triangle if one of the acute angles is 65⁰.
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If cos ∅ = ³/₇, find the degree measure of ∅ to two decimal places.
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Find the value of sin 40⁰ to three decimal places.
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Find sin ∅ given that cos ∅ = ⁴/₅.
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Write the trigonometric formula for finding tan ∅ in terms of opposite (opp), adjacent (adj), and hypotenuse (hyp).
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Identify triangle ABC and triangle EFG as similar or not similar.
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If triangle XYZ is similar to triangle PMN, what is the value of ∠Y when ∠M = 50⁰?
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If triangle XYZ is similar to triangle PMN, which side of triangle PMN corresponds to side x?
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If triangle XYZ is similar to triangle PMN and side x= 7, side y = 5, and side m = 12.5, what is the length of side p?
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Find the exact value of sin ∅.
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Find the exact value of cos ∅.
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Find the exact value of tan ∅.
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Convert 60⁰ to radians.
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Convert ³π/₂ to degrees.
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The base of a 10-foot ladder is placed 3 feet away from the wall of a building. How high does the ladder go up the wall?
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An airplane takes off from a runway at an angle of 15⁰. A fence is 50 feet from the location where the plane took off from the runway. What is the altitude of the airplane when it passes over the fence?
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If a carpenter removes a slanted wall containing a fireplace to make a corner and put up new drywall that is 6 feet long on one corner wall and 8 feet long on the other corner wall, how long was the original slanting wall containing the fireplace?
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Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. What is the angle of inclination from Lily's location to the top of the waterfall?
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Study Notes
Angle Basics
- Vertex angle in a triangle is defined as the angle opposite the base; for ∠DEF, it is ∠E.
- Correct labeling of angles should exclude terms like ∠YXW when labeling using angle points.
Angle Relationships
- Angles ∠X (95⁰) and ∠Y (85⁰) are supplementary if their sum equals 180⁰.
- Complementary angles add up to 90⁰; if ∠A is 42⁰, then ∠B is 48⁰ (90⁰ - 42⁰).
Angle Classifications
- Obtuse angles are greater than 90⁰; ∠C is classified as obtuse given ∠C = 120⁰.
Triangle Angles
- In triangle ABC, if ∠A = 40⁰ and ∠B = 80⁰, then ∠C can be calculated as 60⁰ (180⁰ - 40⁰ - 80⁰).
Degree and Radian Measure
- Conversion factor for degrees to radians is π/180°.
- Example conversion: 60° converts to π/3 radians; conversely, ³π/2 equals 270°.
Trigonometric Functions
- Inverse trigonometric functions are used to find unknown angles; specific conditions must be determined for each case.
- For given right triangle conditions, use relationships such as sin(∅) or cos(∅) to find angle measures.
Right Triangle Properties
- If one acute angle measures 65°, the other is found using 90° - 65°, resulting in 25°.
- If cos(∅) = ³/₇, then ∅ approximately equals 64.62°.
Trigonometric Values
- Values of trigonometric functions can be determined using known angles:
- sin(40°) approximately equals 0.643.
- If cos(∅) = ⁴/₅, then sin(∅) = ³/₅.
Similar Triangles
- Two triangles are not similar when their corresponding angles are not equal.
- If triangle XYZ is similar to triangle PMN, corresponding angles and sides can be utilized to find unknowns.
Problem Solving with Triangles
- Ladder problems utilize the Pythagorean theorem; the height can be found using height = √(ladder² - distance from wall²).
- For the airplane problem, altitude can be found using height = distance to fence * tan(plane's angle).
Applications and Context
- Understanding contextual applications such as angles in real-life situations (e.g. viewing waterfalls, airplane altitudes) enhances comprehension.
- Round results as necessary, especially in practical problems where approximations are acceptable.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards covering key concepts from Test 8 of Abeka Algebra 2 for grade 10. Each card presents a question specific to angle relationships and labeling. Perfect for quick review and strengthening your understanding of algebra and geometry concepts.
