Trigonometry: Solving Right Triangles
24 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a necessary component for solving a right triangle?

  • Knowing the length of the hypotenuse
  • Knowing only one side
  • Knowing all three angles
  • Knowing the measures of two sides (correct)

    • Which function is primarily used in solving right triangles?

  • Algebraic functions
  • Trigonometric functions (correct)
  • Logarithmic functions
  • Exponential functions

    • When naming a right triangle, which letter represents the right angle?

  • The middle letter (correct)
  • The last letter
  • The first letter
  • Any of the three letters

    • What is required to find the values of unknowns in a right triangle using a calculator?

    <p>The calculator must be scientific</p> Signup and view all the answers

    How can angles of elevation and depression be characterized in relation to right triangles?

    <p>They depend on the position of the observer</p> Signup and view all the answers

    Which of the following statements is correct about acute angles in a right triangle?

    <p>The sum of the acute angles is 90 degrees</p> Signup and view all the answers

    What is the process called when finding all measures of a triangle?

    <p>Solving the triangle</p> Signup and view all the answers

    Which of the following is NOT a typical part involved in solving right triangles?

    <p>Calculating the area</p> Signup and view all the answers

    What is the angle of elevation?

    <p>The angle between a horizontal line and the line of sight to an object above the observer</p> Signup and view all the answers

    If the height of an object is greater than the observer's height, which angle is formed?

    <p>Angle of elevation</p> Signup and view all the answers

    In the situation where Jay is flying a kite, how is the length of the string determined?

    <p>By using the height of the kite and the angle the string makes with the ground</p> Signup and view all the answers

    What information is needed to calculate the angle of elevation of the sun when given a pole and its shadow?

    <p>The height of the pole and the length of its shadow</p> Signup and view all the answers

    When Hannah looks at a cat on the ground from the barn, what type of angle is she observing?

    <p>Angle of depression</p> Signup and view all the answers

    What is the relationship between sine and cosine for angles A and B in a right triangle?

    <p>sin A = cos B</p> Signup and view all the answers

    How can the horizontal distance from a tower be calculated if the height of the tower and the angle subtended are known?

    <p>Using the tangent function of the angle and the height</p> Signup and view all the answers

    In a right triangle, if angle A measures 30 degrees, what can be concluded about angle B?

    <p>Angle B must be 60 degrees.</p> Signup and view all the answers

    In solving for the hypotenuse of a right triangle where angle A is known, which trigonometric ratio would commonly be used?

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

    When using the Pythagorean theorem in a right triangle, which formula is used?

    <p>a^2 + b^2 = c^2</p> Signup and view all the answers

    If the length of side a in right triangle ACB is 24.07 cm, what method can be used to find side c?

    <p>Employing the Pythagorean theorem</p> Signup and view all the answers

    When observing an object positioned below the observer's horizontal line of sight, which angle is identified?

    <p>Angle of depression</p> Signup and view all the answers

    How can the angle of elevation and angle of depression be defined in terms of right triangles?

    <p>They describe the angles formed by horizontal and vertical lines.</p> Signup and view all the answers

    If the length of side b in triangle ACB is unknown, which trigonometric function could be most useful if angle A is known?

    <p>tan A</p> Signup and view all the answers

    Which of the following ratios represents the tangent of angle A in right triangle ACB?

    <p>side a/side b</p> Signup and view all the answers

    To find the unknown length of side a at angle A in right triangle ACB, which relationship can be established?

    <p>sin A = a/c</p> Signup and view all the answers

    Study Notes

    Right Triangle Solution

    • Students are expected to solve for unknown parts of a right triangle given known parts.
    • Apply trigonometric functions in problem situations involving right triangles.
    • Use a scientific calculator correctly to find unknown values.
    • Solve problems involving angles of elevation and depression.

    Review Problems

    • Find the exact value of the following expressions, all given in square root format, for example √2/2

    Solving Right Triangles

    • A right triangle is labeled with the sides as a, b and c (hypotenuse), and the angles as A, B, and C (right angle).
    • To solve a right triangle, find the measures of all the angles and sides.
    • Knowing two sides or a side and an acute angle allows solution.

    Definitions of Trigonometric Functions

    • sin A = opposite/hypotenuse
    • cos A = adjacent/hypotenuse
    • tan A = opposite/adjacent
    • sin B = opposite/hypotenuse
    • cos B = adjacent/hypotenuse
    • tan B = opposite/adjacent

    Pythagorean Theorem

    • a² + b² = c²

    Example Problems

    • Example 1: Solve triangle ACB with B = 36°30′ and c = 72.4 cm.

    • The provided example includes sides calculated to the nearest hundredth ( cm, or centimeters).

      • A = 53°30′
      • a ≈ 58.20 cm
      • b ≈ 43.06 cm

    • Example 2: Find unknown parts of triangle ACB if A = 24°45′ and a = 24.07 cm.

      • B ≈ 65°15′
      • c ≈ 57.49 cm
      • b ≈ 52.21 cm

    • Example 3: Solve triangle ACB with c = 201.25 cm, and B = 42°20'33.38''.

      • A = 47°39'26.62''
      • b ≈ 135.55 cm
      • a ≈ 148.75 cm

    Applications of Right Triangles

    • Application scenarios involve angles of elevation and depression.

    Angle of Elevation and Depression

    • Angle of elevation: the angle from the horizontal to a point above an observer.
    • Angle of depression: the angle from the horizontal to a point below an observer.

    Example Application Problem:

    • Example 1: Jay is flying a kite. The string of the kite makes an angle of θ with the ground.

      • If the height of the kite is 21 cm, find the length of the string Jay used.
      • Answer: 31.08 cm

    • Example 2: A pole 60 ft high casts a 48-ft shadow.

    • Find the angle of elevation of the sun.

    • Answer:

    • Calculation needed to solve for the angle.

    • Example 3: Hannah is on top of a 25 ft tall barn.

    • She sees a cat on the ground below.

    • The angle of depression is given(angle).

    • Calculate how many feet the cat needs to walk to reach the barn.

    • Answer: 29.74 ft

    Practice Exercises

    • Exercise 1: Solve the right triangle where c = 37.2 and A = 34°10′.
    • Exercise 2: Solve the right triangle where a = 41.72 and b = 57.34.
    • Exercise 3: Jun is walking along a road. The top of a 35-meter tower subtends an angle with the ground. Find Jun's horizontal distance from the tower.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Solutions Of Right Triangles PDF

    Description

    This quiz focuses on solving right triangles using trigonometric functions and the Pythagorean theorem. Students will practice finding unknown sides and angles using given information and applying their knowledge of scientific calculators. Test your understanding of concepts related to angles of elevation and depression as well.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser