Answer:
m < A = 60º
m < B = 30º
Step-by-step explanation:
The given sides on this triangle are: 6,
, and 12
Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:
x,
, 2x
We can line this up with the given sides. If x is 6, then 2x would be 12.
x :
: 2x = 6 :
: 12
Angle B is across from 6, the shortest side. That also means that it corresponds to x, or the smallest angle in the proportion, 30º.
m < B = 30º
Solving for < A:
Method 1) Sum of Angles in a Triangle
Since we already know that one angle is right and therefore 90º and m < B is 30º, we can subtract these from the total sum of angle measures in a triangle to get the last angle, < A.
180º - 90º - 30º = 60º
m < A = 60º
Method 2) Using the second part of the proportion
Since m < A is across from the second largest side, we know that it is equal to
(
in this question) or 60º in the angle proportion.
This means that m < A = 60º
Let me know if you have any questions!
Answer:
19.4 feet
Step-by-step explanation:
When calculating distances using perpendicular angles, we use trig functions such as Sin, Cos, and Tan.
- Sine is defined in a perpendicular triangle as the ratio of the opposite side to the angle over the hypotenuse.
- Cosine is defined in a perpendicular triangle as the ratio of the adjacent side to the angle over the hypotenuse.
- Tangent is defined in a perpendicular triangle as the ratio of the opposite side over the adjacent side.
Because our angle and know side value are across from each other and we need to know the hypotenuse, we chose to use Sine.
We set up the equation
.
We isolate h by multiplying h across the equal sign and dividing sin (68) across as well. 
And finally we have
. We input to calculator.

See the attached picture below showing the shore with the boat out at sea and the position of the person.
Answer:
Below
I hope its not too complicated

Step-by-step explanation:




Answer:
square inches.
Step-by-step explanation:
<h3>Area of the Inscribed Hexagon</h3>
Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be
inches (same as the length of each side of the regular hexagon.)
Refer to the second attachment for one of these equilateral triangles.
Let segment
be a height on side
. Since this triangle is equilateral, the size of each internal angle will be
. The length of segment
.
The area (in square inches) of this equilateral triangle will be:
.
Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:
.
<h3>Area of of the circle that is not covered</h3>
Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is
inches, the radius of this circle will also be
inches.
The area (in square inches) of a circle of radius
inches is:
.
The area (in square inches) of the circle that the hexagon did not cover would be:
.