COPY: Abeka Algebra 2 Grade 10 - Test 8 Flashcards

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Questions and Answers

In ∠ DEF, which of the following angles is the vertex angle?

  • ∠F
  • There is no vertex angle
  • ∠E (correct)
  • ∠D

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?

<p>obtuse</p> Signup and view all the answers

In triangle ABC, if ∠A = 40⁰ and ∠B = 80⁰, what is the value of ∠C?

<p>60⁰</p> Signup and view all the answers

Which conversion factor is used to convert degrees into radians?

<p>π/₁₈₀⁰ (D)</p> Signup and view all the answers

Find the other acute angle of a right triangle if one of the acute angles is 65⁰.

<p>25⁰</p> Signup and view all the answers

If cos ∅ = ³/₇, find the degree measure of ∅ to two decimal places.

<p>64.62⁰</p> Signup and view all the answers

Find the value of sin 40⁰ to three decimal places.

<p>0.643</p> Signup and view all the answers

Find sin ∅ given that cos ∅ = ⁴/₅.

<p>³/₅</p> Signup and view all the answers

Write the trigonometric formula for finding tan ∅ in terms of opposite (opp), adjacent (adj), and hypotenuse (hyp).

<p>tan ∅ = opp / adj</p> Signup and view all the answers

Identify triangle ABC and triangle EFG as similar or not similar.

<p>not similar</p> Signup and view all the answers

If triangle XYZ is similar to triangle PMN, what is the value of ∠Y when ∠M = 50⁰?

<p>50⁰</p> Signup and view all the answers

If triangle XYZ is similar to triangle PMN, which side of triangle PMN corresponds to side x?

<p>p or MN</p> Signup and view all the answers

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?

<p>17.5</p> Signup and view all the answers

Find the exact value of sin ∅.

<p>⁴/₇</p> Signup and view all the answers

Find the exact value of cos ∅.

<p>√³³/₇</p> Signup and view all the answers

Find the exact value of tan ∅.

<p>⁴√³³/₇</p> Signup and view all the answers

Convert 60⁰ to radians.

<p>π/₃</p> Signup and view all the answers

Convert ³π/₂ to degrees.

<p>270⁰</p> Signup and view all the answers

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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Flashcards

Vertex Angle

The angle formed by the two sides of a triangle, opposite the base.

Supplementary angles

Two angles whose measures add up to 180 degrees.

∠B if ∠A = 42⁰ and ∠A and ∠B are complementary

48 degrees. Complementary angles add up to 90 degrees, so 90 - 42 = 48.

Obtuse Angle

An angle that measures greater than 90 degrees but less than 180 degrees.

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Value of ∠C in triangle ABC if ∠A = 40⁰ and ∠B = 80⁰

60 degrees. The sum of angles in a triangle is 180 degrees, so 180 - 40 - 80 = 60.

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Degrees to Radians Conversion factor

π/₁₈₀

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Acute angle of a right triangle if one angle is 65⁰

25⁰

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Degree of ∅ if cos ∅ = ³/₇

64.62⁰

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Value of sin 40⁰

0.643

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sin ∅ given cos ∅ = ⁴/₅

³/₅

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Formula for tan ∅

tan ∅ = opp / adj

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Similar or not similar triangles

Not Similar

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Value of ∠Y if triangle XYZ ~ triangle PMN and ∠M = 50⁰

50⁰

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Side corresponds to x in triangle PMN if triangle XYZ ~ triangle PMN.

p or MN

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Length of side p if triangle XYZ ~ triangle PMN, side x=7, side y=5, side m=12.5

17.5

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Exact value of sin ∅

⁴/₇

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Exact value of cos ∅

√³³/₇

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Exact value of tan ∅

⁴√³³/₃₃

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60⁰ in radians

π/₃

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³π/₂ in degrees

270⁰

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