If the angles of a triangle are in the ratio 5:3:7,

Question:

If the angles of a triangle are in the ratio 5:3:7, then the triangle is

(a) an acute angled triangle

(b) an obtuse angled triangle

(c) a right angled triangle

(d) an isosceles triangle

Solution:

(a) Given, the ratio of angles of a triangle is 5 : 3 : 7.

Let angles of a triangle be ∠A,∠B and ∠C.

Then, ∠A = 5x, ∠B = 3x and ∠C = 7x

In ΔABC, ∠A + ∠B + ∠C = 180° [since, sum of all angles of a triangle is 180°]

5x + 3x + 7x = 180°

=> 15x = 180°

x = 180°/15= 12°

∠A = 5x = 5 x 12° = 60°

∠B = 3x= 3 x 12°= 36°

and ∠C =7x = 7 x 12° = 84°

Since, all angles are less than 90°, hence the triangle is an acute angled triangle.

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now