3. In triangle RST, Ð S = 90°, Ð T = 30°, RT = 12 cm then find RS and ST.
Answers
Correct Question:
In △ RST, ∠ S = 90°, ∠ T = 30°, RT = 12 cm, then find RS and ST.
Answer:
The length of RS is 6 cm.
The length of ST is 6 √3 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
We have given that,
In △ RST,
∠ S = 90°,
∠ T = 30°,
RT = 12 cm
We have to find RS & ST.
Now, in △ RST,
∠ RST + ∠ SRT + ∠ RTS = 180° - - [ Angle sum property of triangle ]
⇒ 90° + ∠ SRT + 30° = 180°
⇒ ∠ SRT + 120° = 180°
⇒ ∠ SRT = 180° - 120°
⇒ ∠ SRT = 60°
∴ △SRT is a 30°-60°-90° triangle.
Now,
RS = ½ × RT - - [ Side opposite to 30° ]
⇒ RS = ½ × 12
⇒ RS = 6 cm
Now,
ST = ( √3 / 2 ) × RT - - [ Side opposite to 60° ]
⇒ ST = √3 / 2 × 12
⇒ ST = √3 × 12 ÷ 2
⇒ ST = √3 × 6
⇒ ST = 6 √3 cm
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Additional Information:
1. Angle sum property of triangle:
The sum of measures of all three angles of a triangle is 180°.
2. 30°-60°-90° triangle theorem:
In a right angled triangle, if one of the angles is 30°, then the triangle is called as 30°-60°-90° triangle.
And the theorem related to such triangle is 30°-60°-90° triangle theorem.
3. Side opposite to 30°:
The side opposite to the angle 30° in a 30°-60°-90° triangle is always half of the hypotenuse.
4. Side opposite to 60°:
The side opposite to the angle 60° in a 30°-60°-90° triangle is always √3 / 2 of the hypotenuse.
