In a triangle, if the angles are in the ratio 1 ∶ 2 ∶ 3, then the ratio of the corresponding sides is:
1 ∶\(\sqrt 3 \)∶ 2
The correct answer is 1 ∶ \sqrt 3 ∶ 2.
So, 1 + \text{altitude}^2 = 4, which means \text{altitude}^2 = 3, and altitude = \sqrt{3}. This leg is opposite the 60^\circ angle. Thus, the sides opposite the angles 30^\circ, 60^\circ, and 90^\circ are in the ratio 1 : \sqrt{3} : 2. This confirms the result obtained using the Sine Rule for this specific triangle.
Similar Questions
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Given that Δ MAN and Δ CPT are congruent to each other such that ∠M = 75, ∠N = 65, ∠A = 40, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).
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Important Questions from Triangles, Congruence and Similarity
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
If the ratio of corresponding sides of 2 similar triangles is 2 ∶ 3. Then the ratio of their corresponding altitude is :
