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Trigonometry and Right Triangles

Quantitative Aptitude · Maths Bookwise · Geometry & Mensuration

Useful for: SSC CGL

BOOK-GUIDED ORIGINAL SSC MATHS PRACTICE — Trigonometry and Right Triangles

FOUNDATION

For a right triangle, hypotenuse² = base² + perpendicular².

METHOD

Identify the quantities given, choose the exact relationship, calculate in the same unit, then check the answer against the question.

WORKED EXAMPLE 1

A right triangle has perpendicular 1278 cm and hypotenuse 2130 cm. Find base (cm).

Base² = 2130²−1278² = 2903616 = 1704². Base = 1704 cm.

WORKED EXAMPLE 2

A right triangle has perpendicular 885 cm and hypotenuse 1475 cm. Find base (cm).

Base² = 1475²−885² = 1392400 = 1180². Base = 1180 cm.

IMPORTANT EXCEPTION / COMMON TRAP

Hypotenuse is opposite the right angle.

QUICK REVISION

For a right triangle, hypotenuse² = base² + perpendicular².

SEE MORE: https://study.kundali-iq.com/ssc-maths/trigonometry/

For complete timed maths practice, use SSC CGL Test Series → New Maths 100 Mixed Sets or Chapter-wise sets. These are independent original questions, not copied previous-year questions.

Practice MCQs

  1. A right triangle has perpendicular 1278 cm and hypotenuse 2130 cm. Find base (cm).

    1. 1704
    2. 1930
    3. 1591
    4. 1817

    Read chapter notes · Similar questions

    Show answer

    Answer: (a) 1704. Base² = 2130²−1278² = 2903616 = 1704². Base = 1704 cm.

  2. A right triangle has perpendicular 885 cm and hypotenuse 1475 cm. Find base (cm).

    1. 1102
    2. 1258
    3. 1336
    4. 1180

    Read chapter notes · Similar questions

    Show answer

    Answer: (d) 1180. Base² = 1475²−885² = 1392400 = 1180². Base = 1180 cm.

  3. A right triangle has perpendicular 141 cm and hypotenuse 235 cm. Find base (cm).

    1. 188
    2. 212
    3. 200
    4. 176

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    Show answer

    Answer: (a) 188. Base² = 235²−141² = 35344 = 188². Base = 188 cm.

  4. A right triangle has perpendicular 1269 cm and hypotenuse 2115 cm. Find base (cm).

    1. 1580
    2. 1916
    3. 1692
    4. 1804

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    Show answer

    Answer: (c) 1692. Base² = 2115²−1269² = 2862864 = 1692². Base = 1692 cm.

  5. In a right triangle, an acute angle θ has sin θ = 3/5. What is cos θ

    1. 5/4
    2. 3/4
    3. 4/5
    4. 1/5

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    Show answer

    Answer: (c) 4/5. cos θ = √(1 − sin² θ) = √(1 − 9/25) = 4/5, positive for an acute angle.

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Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.