Question

51. In SABC, if Angle B =90". then find the missing quantities in the following table which
are marked by question sign (?):
Sr. No.
AB
BC
AC
12 cm
(?)
37 cm
relatio
21 cm
20 cm
(?)
13)
39 cm
(?)
89 cm
e metho
14)
(?)
55 cm
73 cm

Answer 1

Answer:

angle 1= 90

other angles- 30,30

coz - 30+30+90=180

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Answer 2

Given :- ABC, if ∠B = 90°, then find the missing quantities in the following table :-

AB BC AC

(1) 12 ? 37

(2) 21 20 ?

(3) 39 ? 89

(4) ? 55 73

Solution :-

we know that,

• Angle opposite to right angle = Hypotenuse = AC
• AB² + BC² = AC² (Pythagoras theorem) .

so,

→ AB² + BC² = AC²

→ 12² + BC² = 37²

→ BC² = 37² - 12²

→ BC² = (37 + 12)(37 - 12)

→ BC² = 49 * 25

→ BC² = 7² * 5²

→ BC² = (7 * 5)²

→ BC = 35 (Ans.1)

similarly,

→ AB² + BC² = AC²

→ 21² + 20² = AC²

→ AC² = 441 + 400

→ AC² = 841

→ AC = √(841)

→ AC = 29 (Ans.2)

and,

→ AB² + BC² = AC²

→ 39² + BC² = 89²

→ BC² = 89² - 39²

→ BC² = (89 + 39)(89 - 39)

→ BC² = 128 * 50

→ BC² = 6400

→ BC = √(6400)

→ BC = 80 (Ans.3)

also,

→ AB² + BC² = AC²

→ AB² + 55² = 73²

→ AB² = 73² - 55²

→ AB² = (73 + 55)(73 - 55)

→ AB² = 128 * 18

→ AB² = 2304

→ AB² = √(2304)

→ AB = 48 (Ans.4)

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