Lorenzo ate 25 of his bag of almonds. His 4 friends ate equal shares of the remaining bag of almonds. Which expression represent
1 answer:
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Answer:
Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of and the hypotenuse of
.
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:
Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:
Now use this value in the Law of Sines to find AD:
Recall that and
:
Now that we have the length of AD, we can find the length of AB. The right triangle is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio
, where
is the side opposite to the 30 degree angle and
is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent in this ratio and since AB is the side opposite to the 30 degree angle, it must represent
in this ratio (Derive from basic trig for a right triangle and
).
Therefore, AB must be exactly half of AD: