McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
4. Law of Sines
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Exercise 44 Page 820

Think about a right triangle with the measures of two angles and one of the side lengths.

See solution.

Practice makes perfect

Let's imagine that there is a garden at a nursery school in the shape of a right triangle, and we want to cover this garden with grass. We have the following information about the measures of the garden.

Right triangle
To find out how many square meters of grass is needed, we will find the area of this right triangle. However, we are missing the lengths of the legs. With the measures of two angles and the length of the hypotenuse, we can find the missing lengths. To do so we can recall the Law of Sines.
Let's first use the second and third ratios to find the value of
Solve for
Then we will find the to find the side length opposite to this angle. Let's use the Triangle Angle Sum Theorem.
Now, we can find the value of by using the Law of Sines one more time.
Solve for
Great! Now we can complete our triangle.
completed triangle
Having the lengths of the legs, we can find the area of this right triangle. Let's do it by using the Area Formula!
We have found that about square meters grass are needed to cover the garden of the nursery school.