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

**Answer:**

54°

**Step by Step Explanation:**

- Since, ∠ABC = 90°, we can say that a + b = 90.
- We have been given that

=a b

. Cross multiplying the fractions, we get, 3a = 2b, and on dividing both sides by 3, we get, a =2 3

.2b 3 - Putting this value of a in a + b = 90, we get,

+ b = 90, or2b 3

b = 90. Cross multiplying the fractions again, we get, b =5 3

, or b = 54.90 × 3 5 - Therefore, the angle b is
**54°**.