Find the exact value of side y.

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caledon eNotes educator| Certified Educator

We can use trigonometry to solve this problem.

In any right triangle, we know that the internal angles must add up to 180 degrees.

This means that, no matter how long the sides are, a certain right triangle "shape" will always have the same ratio of sides. These ratios are represented by sine, cosine and tangent.

The cosine of a degree is equal to the adjacent side, divided by the hypotenuse.

For this triangle, the cosine of 60 degrees is equal to Y divided by 10.

cos60 = y/10

To solve for y, we should isolate the variable on one side of the equation. We can do this by multiplying both sides by 10.

10cos60 = y

The cosine of 60 is 0.5

Therefore y = 10(.5)

Y = 5

baxthum8 eNotes educator| Certified Educator

This is a special right triangle called a 30˚-60˚-90˚ right triangle.

The ratios of the sides of a 30˚-60˚-90˚ are `1:sqrt(3):2.`

The length of y, the short side of the right triangle,  is`1/2` the length of the hypotenuse, 10.

Therefore the length of y is `10-:2` = 5

Side y is 5 units long.

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