Download Right Angle Trigonometry For any triangle, the sum of the angles a

Right Angle Trigonometry
For any triangle, the sum of the angles a, b, and c is 180 degrees.
If a triangle has three equal sides, each of length x, then each angle is 60 degrees.
A building is 100 feet from a point on the level ground. A cable is stretched to the top of the building,
and the cable make an angle of 30 degrees with the ground. How tall is the building, and how long is the
cable? An antenna is at the edge of the roof, and the top of the antenna makes an angle of 35 degrees
with the ground when viewed from the point 100 feet from the building. How long is the antenna?
Call the height y.
Then
so y = 100 tan(30o ) =
100
p
3
y
= tan(30o )
100
= 57:735 feet. Make sure your calculator is in degrees, not radian, mode.
100
= cos(30o )
r
where r is the length of the cable , so
100
100
= 115:47 feet.
= p
o
cos(30 )
( 3=2)
Now call y2 = the height from the ground to the top of the antenna. Then
r=
y2
= tan(35o )
100
so y2 = 100 tan(35o ) = 70:0207
The height of the antenna is y2 ¡ y = 70:0207 ¡ 57:735 ¼ 12:29 feet.
More facts about right triangles:
Given two sides of a right triangle, you can ¯nd the third side using the Pythagorean Theorem.
The inverse sine, sin¡1 (a=c) is the angle whose sine is a/c.
The inverse cosine,cos¡1 (b=c) is the angle whose cosine is b/c
The inverse tangent, tan¡1 (a/b) is the angle whose tangent is a/b.
Examples:
sin¡1 (1=2) is the angle whose sine is 1/2, and that angle is 30o , so sin¡1 (1=2) = 30o .
tan¡1 (1) is the angle whose tangent is 1, and that angle is 45o , so tan¡1 (1) = 45o .
By using your calculator, tan¡1 (4=12) = 18:4o approximately.