Let abcd be a square, and let m and n be the midpoints of bc and cd, respectively. the value of \sin \angle man can be expressed in the form m/n, where m and n are relatively prime positive integers. find m + n.

s

Step-by-step explanation:

Hi there! I've graphed a square, with its midpoints so that you can visualize it better (below).

1) Starting with a square ABCD, a square since it has four equal angles, its sides (s) they have the same size.

2) The first statement says the sin M∠AN can be expressed in terms of and m, and n are relatively prime positive integers, in other words, there is only one divisor of m and n: 1. And n can never be zero.

With that in mind, let's start calculating:

Sin MAN=

m=?

Well, m is the hypotenuse of Δ AND

Then,

n=?

Well, n is also a hypotenuse. But the Δ ABM one.

Then, similarly to m

n²=(s)²+(s²/2)²

n²=s²+s²/4

n²=5s²/4

n=

3) Finally, we're now able to find the sum m +n

m + n = ?

And review and test our work.

In the first part of the question, it was said the value of the sin of MAN, i.e. the sin of ∠A = . The distance between a midpoint and a vertex is the same. So, MA = NA

You can choose a number, let's say a square whose sides measure 4 units and do the test.

So MA = m and n=NA and sin ∠A is 90º

sin ∠A = MA/NA

sin 90º =MA/NA

1=1 correct

if the probability is 1/12, 75 people will receive a $25 gift card

step-by-step explanation:

35x 3= 105

step-by-step explanation:

35+35= 70   70 + 35= 105