The more we study trigonometric applications, the more we discover that the applications are countless. Some are flat, diagram-type situations, but many applications in calculus, engineering, and physics involve three dimensions and motion.
Finding an altitude
Find the altitude of the aircraft in the problem introduced at the beginning of this section, shown in
[link] . Round the altitude to the nearest tenth of a mile.
To find the elevation of the aircraft, we first find the distance from one station to the aircraft, such as the side
and then use right triangle relationships to find the height of the aircraft,
Because the angles in the triangle add up to 180 degrees, the unknown angle must be 180°−15°−35°=130°. This angle is opposite the side of length 20, allowing us to set up a Law of Sines relationship.
The distance from one station to the aircraft is about 14.98 miles.
Now that we know
we can use right triangle relationships to solve for
The aircraft is at an altitude of approximately 3.9 miles.
The diagram shown in
[link] represents the height of a blimp flying over a football stadium. Find the height of the blimp if the angle of elevation at the southern end zone, point A, is 70°, the angle of elevation from the northern end zone, point
is 62°, and the distance between the viewing points of the two end zones is 145 yards.
The Law of Sines can be used to solve oblique triangles, which are non-right triangles.
According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side.
There are three possible cases: ASA, AAS, SSA. Depending on the information given, we can choose the appropriate equation to find the requested solution. See
[link] .
The ambiguous case arises when an oblique triangle can have different outcomes.
There are three possible cases that arise from SSA arrangement—a single solution, two possible solutions, and no solution. See
[link] and
[link] .
The Law of Sines can be used to solve triangles with given criteria. See
[link] .
The general area formula for triangles translates to oblique triangles by first finding the appropriate height value. See
[link] .
There are many trigonometric applications. They can often be solved by first drawing a diagram of the given information and then using the appropriate equation. See
[link] .
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
