Question

In a right-angled triangle, the two acute angles are in the ratio 4:5. Find these angles​

Answer 1

✽ Question ✽

In a right-angled triangle, the two acute angles are in the ratio 4:5. Find these angles.

✽ Given ✽

The triangle is right angled.

The acute angles are in the ratio 4:5.

✽ To find ✽

The angles.

✽ Solution ✽

Let the acute angles are 4x° and 5x°.

The third angle is 90°.

As we know that the sum of all angles of a triangle is 180°, we can say-

4x + 5x + 90 = 180

→ 9x = 180-90

→ 9x = 90

→ x = 90/9

→ x = 10

✽ Hence ✽

x = 10

One angle = 4x° = (4×10)° = 40°

Other angle = 5x° = (5×10)° = 50°

✽ Therefore ✽

The measure of the acute angles are 40° and 50° respectively.

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✽ Verification ✽

4x + 5x + 90 = 180

→ 40 + 50 +90 = 180

→ 180 = 180

So, L.H.S = R.H.S.

Hence, verified.

◎ Hope this helps you. ◎