Question 136

The angles of a triangle are $$30^\circ, 60^\circ$$ and $$90^\circ$$. Then the sides of the triangle are in the ratio

Solution

Share

Let $$\angle$$A = $$30^\circ$$, $$\angle$$B = $$60^\circ$$ and $$\angle$$C = $$90^\circ$$

sin$$30^\circ$$ = $$\frac{BC}{AB}$$

$$\frac{1}{2}$$ = $$\frac{BC}{AB}$$

Let BC = x and AB = 2x

AC = $$\sqrt{AB^{2} - BC^{2}}$$

AC = $$\sqrt{3}x$$

Now, 

Required ratio = BC: AC: AB = x: $$\sqrt{3}x$$: 2x = 1: $$\sqrt{3}$$: 2

Get AI Help

View More Questions From Geometry

Create a FREE account and get:

  • Download Maths Shortcuts PDF
  • Get 300+ previous papers with solutions PDF
  • 500+ Online Tests for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Mensuration QuestionsCAT Number Series QuestionsCAT Profit and Loss QuestionsCAT Percentages QuestionsCAT Time, Speed and Distance Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Routes And Networks QuestionsCAT Quant Based DI QuestionsCAT Quant Based LR QuestionsCAT Venn Diagrams QuestionsCAT Puzzles Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Odd One Out QuestionsCAT Para Summary QuestionsCAT Verbal Ability QuestionsCAT Grammar and Sentence Correction QuestionsCAT Reading Comprehension Questions

Free CAT Quant Questions

CAT Profit And LossCAT Data SufficiencyCAT Number SystemsCAT Averages Mixtures AlligationsCAT Linear EquationsCAT Simple Interest Compound InterestCAT InequalitiesCAT RemaindersCAT Time And WorkCAT PercentagesCAT Venn DiagramsCAT Time, Speed and DistanceCAT Averages, Ratio and ProportionCAT Number SeriesCAT MiscellaneousCAT Probability, CombinatoricsCAT GeometryCAT ArithmeticCAT AveragesCAT LogarithmsCAT Quadratic EquationsCAT Coordinate GeometryCAT Progressions and SeriesCAT AlgebraCAT Profit and LossCAT MensurationCAT Functions, Graphs and StatisticsCAT Logarithms, Surds and IndicesCAT Time Speed Distance

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!

Enroll Now
Ask AI