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PLEASE EXPLAIN!

 

 Feb 6, 2024

Best Answer 

 #1
avatar+1618 
+1

Hypotenuse = 3sqrt(15)

Shorter Leg = 3 sqrt(6)

By pythagorean theorem, Longer Leg = 9

Let the point between the hypotenuse and the shorter leg be A. We know that point A must have the largest acute angle in the triangle by construction.

Using any trig function (preferably a easy-calculation one), such as sinA, we can use the inverse function of it to find the angle.

sinA = opposite/hypotenuse = 9/3sqrt(15) = 3sqrt(15)/15 = sqrt(15)/5

 

Then angle A = arcsin(sqrt(15)/5) = 0.886 radians = 50.8 degrees.

 Feb 6, 2024
 #1
avatar+1618 
+1
Best Answer

Hypotenuse = 3sqrt(15)

Shorter Leg = 3 sqrt(6)

By pythagorean theorem, Longer Leg = 9

Let the point between the hypotenuse and the shorter leg be A. We know that point A must have the largest acute angle in the triangle by construction.

Using any trig function (preferably a easy-calculation one), such as sinA, we can use the inverse function of it to find the angle.

sinA = opposite/hypotenuse = 9/3sqrt(15) = 3sqrt(15)/15 = sqrt(15)/5

 

Then angle A = arcsin(sqrt(15)/5) = 0.886 radians = 50.8 degrees.

proyaop Feb 6, 2024

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