Heron’s formula finds the area of oblique triangles in which sides
$\text{\hspace{0.17em}}a,b\text{,}$ and
$\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ are known.
where
$\text{\hspace{0.17em}}s=\frac{\left(a+b+c\right)}{2}\text{\hspace{0.17em}}$ is one half of the perimeter of the triangle, sometimes called the semi-perimeter.
Using heron’s formula to find the area of a given triangle
Find the area of the triangle in
[link] using Heron’s formula.
Use Heron’s formula to find the area of a triangle with sides of lengths
$\text{\hspace{0.17em}}a=29.7\text{\hspace{0.17em}}\text{ft},b=42.3\text{\hspace{0.17em}}\text{ft},\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}c=38.4\text{\hspace{0.17em}}\text{ft}.$
Area = 552 square feet
Applying heron’s formula to a real-world problem
A Chicago city developer wants to construct a building consisting of artist’s lofts on a triangular lot bordered by Rush Street, Wabash Avenue, and Pearson Street. The frontage along Rush Street is approximately 62.4 meters, along Wabash Avenue it is approximately 43.5 meters, and along Pearson Street it is approximately 34.1 meters. How many square meters are available to the developer? See
[link] for a view of the city property.
Find the measurement for
$\text{\hspace{0.17em}}s,\text{\hspace{0.17em}}$ which is one-half of the perimeter.
Find the area of a triangle given
$\text{\hspace{0.17em}}a=4.38\text{\hspace{0.17em}}\text{ft}\text{\hspace{0.17em}},b=3.79\text{\hspace{0.17em}}\text{ft,}\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}c=5.22\text{\hspace{0.17em}}\text{ft}\text{.}$
about 8.15 square feet
Access these online resources for additional instruction and practice with the Law of Cosines.
The Law of Cosines defines the relationship among angle measurements and lengths of sides in oblique triangles.
The Generalized Pythagorean Theorem is the Law of Cosines for two cases of oblique triangles: SAS and SSS. Dropping an imaginary perpendicular splits the oblique triangle into two right triangles or forms one right triangle, which allows sides to be related and measurements to be calculated. See
[link] and
[link] .
The Law of Cosines is useful for many types of applied problems. The first step in solving such problems is generally to draw a sketch of the problem presented. If the information given fits one of the three models (the three equations), then apply the Law of Cosines to find a solution. See
[link] and
[link] .
Heron’s formula allows the calculation of area in oblique triangles. All three sides must be known to apply Heron’s formula. See
[link] and See
[link] .
Section exercises
Verbal
If you are looking for a missing side of a triangle, what do you need to know when using the Law of Cosines?
two sides and the angle opposite the missing side.
If you are looking for a missing angle of a triangle, what do you need to know when using the Law of Cosines?
Explain what
$\text{\hspace{0.17em}}s\text{\hspace{0.17em}}$ represents in Heron’s formula.
$\text{\hspace{0.17em}}s\text{\hspace{0.17em}}$ is the semi-perimeter, which is half the perimeter of the triangle.
Questions & Answers
Calculate price elasticity of demand and comment on the shape of the demand curve of a good ,when
its price rises by 20 percentage, quantity demanded falls from 150 units to 120 units.
5 %fall in price of good x leads to a 10 % rise in its quantity demanded. A 20 % rise in price of good y
leads to do a
10 % fall in its quantity demanded. calculate price elasticity of demand of good x and good y. Out of the
two goods which one is more elastic.
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
sorry it the mistake answer it is question
Sosna
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
The formula for calculation income elasticity of demand is the percent change in quantity demanded divided by the percent change in income.
n a perfectly competitive market, price equals marginal cost and firms earn an economic profit of zero. In a monopoly, the price is set above marginal cost and the firm earns a positive economic profit. Perfect competition produces an equilibrium in which the price and quantity of a good is economic
because monopoly have no competitor on the market and they are price makers,therefore,they can easily increase the princes and produce small quantity of goods but still consumers will still buy....
macroeconomics,microeconomics,positive economics and negative economics
Gladys
what are the factors of production
Gladys
process of production
Mutia
Basically factors of production are four (4) namely:
1. Entrepreneur
2. Capital
3. Labour and;
4. Land
but there has been a new argument to include an addition one to the the numbers to 5 which is "Technology"
Elisha
what is land as a factor of production
Gladys
what is Economic
Abu
economics is how individuals bussiness and governments make the best decisions to get what they want and how these choices interact in the market
Nandisha
Economics as a social science, which studies human behaviour as a relationship between ends and scarce means, which have alternative uses.
Yhaar
Economics is a science which study human behaviour as a relationship between ends and scarce means
John
Economics is a social sciences which studies human behavior as a relationship between ends and scarce mean, which have alternative uses.....
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.