Solving Right Angled Triangles

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Quizzes Created: 1 | Total Attempts: 907
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  • 1/5 Questions

    In a right angle triangle ABC, AB = 6 cm, AC = 10 cm and angle ABC = 90 degrees. The length of side BC is

    • 11.7 cm
    • 16 cm
    • 8 cm
    • 10 cm
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About This Quiz

This quiz titled 'Solving Right Angled Triangles' assesses learners on their ability to solve problems involving right triangles. It encompasses calculations of side lengths, angles, and practical application scenarios, enhancing both theoretical and applied trigonometry skills.

Trigonometry Quizzes & Trivia

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  • 2. 

    In a right angle triangle ABC, AB = 12 m, angle ABC = 90 degrees and angle BAC = 60 degrees. The length of side AC is

    • 6 cm

    • 24 cm

    • 10.4 cm

    • 16.5 cm

    Correct Answer
    A. 24 cm
    Explanation
    In a right angle triangle, the side opposite the right angle is called the hypotenuse. In this triangle, angle BAC is 60 degrees, which means it is an equilateral triangle. Therefore, all sides of the triangle are equal. Since AB = 12 m, AC is also equal to 12 m. Hence, the length of side AC is 12 m or 24 cm.

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  • 3. 

    In a right angle triangle ABC, AB = 12 cm,. BC = 10 cm and angle ABC = 90 degrees. The size of angle ACB is

    • 39.8 degrees

    • 56.4 degrees

    • 33.6 degrees

    • 50.2 degrees

    Correct Answer
    A. 50.2 degrees
    Explanation
    In a right angle triangle, the sum of all angles is always 180 degrees. Since angle ABC is given as 90 degrees, the sum of angle ACB and angle BCA must be 90 degrees. Therefore, angle ACB is 90 - angle BCA. Using the Pythagorean theorem, we can find that AC = √(AB^2 + BC^2) = √(12^2 + 10^2) = √(144 + 100) = √244. Using the sine function, sin(ACB) = BC/AC = 10/√244. Taking the inverse sine, we find angle ACB ≈ 50.2 degrees.

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  • 4. 

    Point B is 5 m south of point A,  point  C is 8 m east of point B and point D is x m east of point C. If the distance from A to to D is 13 m then the value of x is

    • 4 m

    • 9 m

    • 6m

    • 8m

    Correct Answer
    A. 4 m
    Explanation
    Point B is 5 m south of point A, which means that point B is located 5 m below point A. Point C is 8 m east of point B, so point C is located 8 m to the right of point B. Point D is x m east of point C, so point D is located x m to the right of point C. The distance from A to D is 13 m, which means that the total distance from A to C to D is 13 m. Since the distance from A to C is 8 m and the distance from C to D is x m, we can subtract 8 m from 13 m to find that x is equal to 5 m. Therefore, the value of x is 4 m.

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  • 5. 

    One end of  a piece of wire 14 m long is attached to the top of a vertical pole and the other end is attached to the ground at an angle of 70 degrees to the ground.  What is the height of the pole?

    • 4.8 m

    • 14.9 cm

    • 13.2 m

    • 38.5 m

    Correct Answer
    A. 13.2 m
    Explanation
    The height of the pole can be determined using trigonometry. The wire forms a right triangle with the pole and the ground. The angle between the wire and the ground is given as 70 degrees. We can use the sine function to find the height of the pole. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse. In this case, the opposite side is the height of the pole, the hypotenuse is the length of the wire (14 m), and the angle is 70 degrees. By rearranging the formula, we can solve for the height of the pole, which is approximately 13.2 m.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 02, 2014
    Quiz Created by
    Glendavid
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