∠ABC is a right angle and a:b = 2:3. Find b.


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Answer:

54°

Step by Step Explanation:
  1. Since, ∠ABC = 90°, we can say that a + b = 90.
  2. We have been given that  
    a
    b
      =  
    2
    3
     . Cross multiplying the fractions, we get, 3a = 2b, and on dividing both sides by 3, we get, a =  
    2b
    3
     .
  3. Putting this value of a in a + b = 90, we get,  
    2b
    3
      + b = 90, or  
    5
    3
     b = 90. Cross multiplying the fractions again, we get, b =  
    90 × 3
    5
     , or b = 54.
  4. Therefore, the angle b is 54°.

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