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
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
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)?
Observe the given figure and find the value of S.
In ΔTAP, ∠TAP = 60°, TA = 6 cm, AP = 8 cm. K is the midpoint of AP. A line from K is produced to meet TP at O such that ∠AKO = 120°. Find the length of OK.
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).
If M is the mid-point of the side BC of ABC, and the area of ABM is 19 cm2 , then the area of ABC is:
In Δ PQR, S and T are points on the sides PQ and PR, respectively, such that Δ PST is similar to Δ PRQ. If m ∠PQR = 47°, then find m ∠STR.
If Δ ABC ~ ΔDEF, ∠A = 47°, and ∠E = 63°, then what is the measure of ∠C?
It is given that ΔABC ∼ ΔYZX and Ar ΔABC : Ar ΔXYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?
In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD = 10 cm, AD = 4 cm and BC = 5 cm, then DE = ?
Important Questions from Triangles, Congruence and Similarity
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
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:
