Question

. In a right trungle, the two acute angles are in the ratio 4:5. What is a
measure of the smallest acute angle?​

Answer 1

★GIVEN★

In a right angle triangle, the two acute angles are in the ratio 4:5.

★To Find★

Measure of the smallest acute angle.

★SOLUTION★

We know that a right angled triangle has a right angle and two acute angles.

We also know that sum of all angles of a triangle is 180°.

Let the acute angles be 4x, 5x.

According to the question,

$\large\implies{\sf{4x\degree+5x\degree+90\degree=180\degree}}$

$\large\implies{\sf{4x+5x+90=180}}$

$\large\implies{\sf{9x=180-90}}$

$\large\implies{\sf{9x=90}}$

$\large\implies{\sf{x=\dfrac{90}{9}}}$

$\large\implies{\sf{x=\dfrac{\cancel{90}}{\cancel{9}}}}$

$\large\therefore\boxed{\bf{x=10.}}$

The angles are:-

1. 4x = 4 × 10 = 40°
2. 5x = 5 × 10 = 50°
3. 90°

★VERIFICATION★

$\large\implies{\sf{40\degree+50\degree+90\degree=180\degree}}$

$\large\implies{\sf{40+50+90=180}}$

$\large\implies{\sf{180\degree=180\degree}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

So, the smallest acute angle is 40°.