Question

A 15-foot flagpole leans slightly, such that it makes an 80° angle with the ground. The shadow of the flagpole is 10 feet long when the sun has an unknown angle of elevation. How could the angle of elevation of the sun, x, be determined?

Answer 1

By determining the length of TV using TV^2=15^2+10^2-2(15)(10)cos80, and then determining the value of x using 15^2=TV^2+10^2-2(TV)(10)cosx.

Answer 2

The angle of elevation of the sun x is determined by $15^2=TV^2+10^2-2(TV)(10)cos(x)$.

We have given that,

A 15-foot flagpole leans slightly, such that it makes an 80° angle with the ground.

The shadow of the flagpole is 10 feet long when the sun has an unknown angle of elevation.

What is the angle of elevation?

An angle of elevation is defined as an angle between the horizontal plane and line of sight from the observer's eye to some object above.

By determining the length of TV using

$TV^2=15^2+10^2-2(15)(10)cos80,$

$TV^2=225+100-300\cos \left(80^{\circ \:}\right)}\\=225+100-300\cos \left(80^{\circ \:}\right)$

and then determining the value of x using

$15^2=TV^2+10^2-2(TV)(10)cosx.$

Therefore, The angle of elevation of the sun x is determined by $15^2=TV^2+10^2-2(TV)(10)cos(x).$

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