Given sin ∅ 3/5, find a, the other angle in the right triangle
The answer is 30,60,90
How is this someone explain?
Draw it
it is a right triangle
the hypotenuse is 5
one side is 3
so the other side is sqrt(25-9) = 4
so the sides are 3, 4, 5
30 60 90 is in the ratios
1 , sqrt 3, 2
In fact
∅ = sin^-1 (3/5) = 36.9 degrees
90-∅ = other angle = 53.1 degrees
Thank you
You are welcome.
To find the other angle in a right triangle when given the sine of one of the angles, you can use the inverse sine function, also known as arcsine.
In this case, you're given that sin ∅ is equal to 3/5. To find the angle ∅, you can take the inverse sine of 3/5:
∅ = arcsin(3/5)
Using a calculator or trigonometric table, you can find the value of arcsin(3/5) to be approximately 36.87 degrees.
However, it seems that the answer you provided, 30, 60, 90, does not match the calculation. In a 30-60-90 triangle, the ratios of the sides are as follows:
sin(30 degrees) = 1/2
sin(60 degrees) = √3/2
So, if sin ∅ is equal to 3/5, it does not correspond to the angles in a 30-60-90 triangle. Please double-check the given information or provide further details if necessary.