Answer:
A
Step-by-step explanation:
Recall that sin = opposite over hypotenuse
For ∠A we are already given its opposite side length ( 2 ) however the hypotenuse has not been identified.
The triangle shown is a right triangle ( indicated by the little square on the bottom left ) which means that we can find a missing side length, more specifically the hypotenuse, using the Pythagorean theorem
where a and b = legs and c = hypotenuse
we are given that the legs = 2 and 4 and need to find the hypotenuse
That being said we plug in what we are given and solve for c
![2^2+4^2=c^2\\2^2=4\\4^2=16\\16+4=20\\20=c^2](https://tex.z-dn.net/?f=2%5E2%2B4%5E2%3Dc%5E2%5C%5C2%5E2%3D4%5C%5C4%5E2%3D16%5C%5C16%2B4%3D20%5C%5C20%3Dc%5E2)
In order to get the exact value of c we must get rid of the exponent.
To do so we can take the square root of both sides
![\sqrt{20} =\sqrt{20} \\\sqrt{c^2} =c\\c=\sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B20%7D%20%3D%5Csqrt%7B20%7D%20%5C%5C%5Csqrt%7Bc%5E2%7D%20%3Dc%5C%5Cc%3D%5Csqrt%7B20%7D)
hence, the hypotenuse = √20
Now lets look back at the question
<em>Find sin∠A to the nearest hundredth. </em>
well remember sin = opposite over hypotenuse
The opposite of sin∠A is 2 and the hypotenuse is √20
Hence, sin∠A =
which is equivalent to .447213595
Our last step is to round to the nearest hundredth
We get the sin∠A = .45