Question

Complete the following activity.
(1) In ∆RST, angleS = 90°, angle T = 45°, RT = 12 cm. Find RS and ST.

In ∆ RST, angleT = 45°, angleS = 90°,
angleR=
According to 45°- 45°-90° theorem


RS =
1/√2 x
=
st = ×rt
=
​

Answer 1

Answer:

△RST

∠S=90

∘

∠T=45

∘

RT=12cm

∠R=180

∘

−∠S−∠T [∵ Sum of all 3 sides of a triangle in supplementary]

=180

∘

−90

∘

−45

∘

∠R=45

∘

sinT=

RT

RS

⇒sin45

∘

=

12

RS

⇒

2

1

=

12

RS

⇒RS=6

2

∵∠R=∠T

⇒ST=RS [Sides opposite in equal angle are equal]

⇒ST=6

2

[From above 2 equations]

Hence RS=6

2

ST=6

2