Answer:
SOH CAH TOA
Step-by-step explanation:
<em>Finding sides (first 2 pictures)</em>
For finding sides of a triangle, you first must "map" the triangle using the given angle as a reference. In this case (for the first picture) use the angle with the measure of 32. The side directly across from the reference angle is the opposite. Label it "O." The side directly across from the right angle is the hypotenuse. Label it "H." Thus, the other side (12) must be the adjacent side. Label it "A." Since you are given
and
, and you know that
is the hypotenuse and
is the adjacent side, you use the CAH operation, meaning
.
Set it up like so:

Use order of operations:

Plug that in your calculator and that's your answer.
<em>Finding angles (last 3 pictures)</em>
In the third picture, you are given two sides and x. When finding angles, you <em>only</em> use what you are given. However, instead of using sin, cos, tan, you must use the inverse, which is
and so on.
Since you are trying to find x, you still use it as your reference angle. 20 is the hypotenuse and 11 is adjacent. Don't worry about the other side- it's not necessary unless it's given. Since you are given the hypotenuse and the adjacent, you use the
property. (inverse)
It's done like so:

Put that in your calculator, and that's the answer! The rest of the angle problems are done the same way, just using different sides.
8 is the number when triples and then 8 is subtracted to equal 16
The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.
Step-by-step explanation:
The given is,
Future value, F = $15,000
Interest, i = 5.9%
( compounded continuously )
Period, t = 12 years
Step:1
Formula to calculate the present with compounded continuously,
...............(1)
Substitute the values in equation (1) to find the P value,
( ∵
)

( ∵
)
We change the P (Present value) into the left side,


≅ 7389.43
P = $ 7389.43
Result:
The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.
We want to simplify √(-48).
Note that
i² = -1 by definition.
Therefore

Answer: c.