Question

the difference between the two acute angles of a right angled triangle is 2pie /5 radians express the angles in degrees ​

Answer 1

Answer:

The sum of the two acute angles of a right triangle is 90∘90∘

Difference between the actute angles

π15c=(π15×180π)∘π15c=(π15×180π)∘

⇒12∘⇒12∘

Let the two acute angles be x∘x∘ and y∘y∘ then,

x+y=90∘x+y=90∘--------(1)

x−y=12∘x−y=12∘--------(2)

____________________

2x=102∘2x=102∘

x=51∘x=51∘

⇒y=39∘

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Answer 2

Answer:

9degree

Step-by-step explanation:

If the difference between two acute angles of a right angled triangle is 2π5, we want to determine the measure of the smallest angle in degrees.

Let the measure of the smallest angles in radians be θ.

⇒ The measure of the other acute angled triangle is π2−θ.

The difference between two acute angles of a right angled triangle is 2π5.

⇒(π2−θ)−θ=2π5⇒θ=12(π2−2π5)=π20.

⇒ The measure of the the smallest angle in degrees is π20⋅180π=9o.