At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account
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:
Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.