A flagpole casts a 12ft long shadow and the sun is currently at an angle of elevation of 53°. How tall is the flagpole?

12.59

88

feet

.

Step-by-step explanation: From the diagram you can see that we have constructed a right triangle, with height A and base 15.

Length of shadow = 15 feet.

Height of flagpole = A.

We know the angle of elevation is

40

∘

. Using this angle and the tangent ratio, we can find A.

tan

(

40

∘

)

=

opposite

adjacent

=

A

15

∴

tan

(

40

∘

)

=

A

15

Rearranging:

A

=

15

tan

(

40

∘

)

By calculator:

A

=

12.59

feet. ( 2 d.p.)

cheater

step-by-step explanation:

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed