A block of flats is 100m away from a cellphone tower. Someone stands at
. They measure the angle from
up to the top of the tower
to be 62
. This is the angle of elevation. They then measure the angle from
down to the bottom of the tower at
to be 34
. This is the angle of depression.What is the height of the cellph one tower correct to 1 decimal place?
To find the height of the tower, all we have to do is find the length of
and
. We see that
and
are both right-angled triangles. For each of the triangles, we have an angle and we have the length
. Thus we can calculate the sides of the triangles.
We are given that the length
is 100m.
is a rectangle so
.
Use your calculator to find that
. Using this, we find that
m
We have that the height of the tower
.
Maps and plans
Maps and plans are usually scale drawings. This means that they are an exact copy of the real thing, but are usually smaller. So, only lengths are changed, but all angles are the same. We can use this idea to make use of maps and plans by adding information from the real world.
A ship approaching Cape Town Harbour reaches point A on the map, due south of Pretoria and due east of Cape Town. If the distance from Cape Town to Pretoria is 1000km, use trigonometry to find out how far east the ship is from Cape Town, and hence find the scale of the map.
We already know the distance between Cape Town and
in blocks from the given map (it is 5 blocks). Thus if we work out how many kilometers this same distance is, we can calculate how many kilometers each block represents, and thus we have the scale of the map.
Let us denote Cape Town with
and Pretoria with
.
We can see that triangle
is a right-angled triangle. Furthermore, we see that the distance
and distance
are both 5 blocks. Thus it is an isoceles triangle, and so
.
To work out the scale, we see that
Mr Nkosi has a garage at his house, and he decides that he wants to add a corrugated iron roof to the side of the garage. The garage is 4m high, and his sheet for the roof is 5m long. If he wants the roof to be at an angle of
, how high must he build the wall
, which is holding up the roof? Give the answer to 2 decimal places.
We see that the triangle
is a right-angled triangle. As we have one side and an angle of this triangle, we can calculate
. The height of the wall is then the height of the garage minus
.
If
=5m, and angle
, then
Thus we have that the height of the wall
.
Applications of trigonometric functions
A boy flying a kite is standing 30 m from a point directly under the
kite. If the string to the kite is 50 m long, find the angle ofelevation of the kite.
What is the angle of elevation of the sun when a tree 7,15 m tall
casts a shadow 10,1 m long?
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .