A Trigonometric Path into the Land of Regular Pentagons - National ...

9. 10.
x
22 ◦
13
45
o 45
tan 22 =
x
37 ◦ o x
45
cos37 =
.40 =
x
13
x
x
.40x
= 45
.8 = 13
.40x
45
=
(.8)(13) = x
.40 .40
x = 10.4
x = 112.5
11. A building cast a 21m long shadow. The angle on the ground from the end of the
shadow to the top of the building is 38º. What is the height of the building?
o x
tan 38 =
21
x
.78 =
21
(.78)(21) = x
x = 16.38
The building is 16.38 m tall.
Building = x
38 ◦
Shadow = 21 m
12. A 5m ladder leans against a building. The ground and the bottom of the ladder form a
70º angle. How tall is the building?
o x
sin 70 =
5
x
Ladder = 5 m
.94 =
Building = x
5
(.94)(5) = x
x = 4.7
The building is 4.7 m tall.
13. A support cable for a radio tower is anchored 30 ft from the base of the tower. The
ground and the cable form a 50º angle. How long is the cable?
o 30
cos50 =
x
30
.64 =
x
.64x
= 30
.64x
30
=
.64 .64
x = 46.9
The cable is 46.9 ft long.
Cable = x
50 ◦
70 ◦
30 ft