Question

the difference between the measures of two acute angles of a right angled triangle is 72 find the measures of the angles in radian​

Answer 1

Given :-

• Difference between the measures of two acute angles of a right angled triangle is 72°.

To Find :-

• find the measures of the angles in radian ..

Solution :-

Since It a right angle ∆, That Means one Angle is 90°.

So,

→ Sum of Rest two angles = 180° - 90° = 90°.

Now, Let us assume That, Rest two acute angles are a & b. where a > b.

Than,

→ a + b = 90° ---------------- Equation (1)

→ a - b = 72° (Given) ------------- Equation (2)

Adding Both Equations we get,

→ a + b + a - b = 90 + 72

→ 2a = 162°

→ a = 81° .

Putting in Equation (1) now,

→ 81 + b = 90

→ b = 90 - 81

→ b = 9°.

Hence, Rest Two acute angles are 9° and 81°..

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Now, we have to convert These angles into Radian.

we know that :-

☛ 180° = π radian

So,

➼ 180° = π radian

➼ 1 ° = (π/180) radian

➼ 9° = (π/180) * 9 = (π/20) rad.. (Ans).

Similarly,

➻ 81° = (π/180) * 81 = (9π/20) rad (Ans).

Hence, Measures of the Rest two acute angles in radian is (π/20)rad. & (9π/20)rad. .

Answer 2

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Problem-}}}}}}$

The difference between the measures of two acute angles of a right angled triangle is 72 find the measures of the angles in radian

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer-}}}}}}$

________________________________

We know right angle = 90°

Sum of two angles would be = 180° - 90° = 90°

So, let the other two acute angle be x & y, where x >y

________________________________

=> a + b = 90° ___________equ(1)

=> a - b = 72° ___________equ(2)

__________________________________

By adding both equations,we get-

=> a + b + a - b = (90 + 72)°

=> 2a = 162°

=> A= 81°

Putting equ(1) ,

=> 81° + b = 90°

=> B = (90- 81)°

=> B = 9°

________________________________

Hence,the other two acute angles are 81° and 9°

________________________________

Now,we have to convert them into radians,

We know that 180° = π radian

______________________________

converting 9° angle to radian

=> 180° = π radian

=> 1° = ( π/180) radian

=> 9° = (π/180)×9 raidan

=>(π/20) radian

________________________________

converting 81° angle to radian

=> 180° = π radian

=> 1° = (π/180)

=> 81° = (π/180)×81 radian

=> (9π/20) radian

______________________________

Hence,the rest two acute angles in radian are (π/20) radian and (9π/20) radian