Transcript Advanced Precalculus Notes 7.1 Right Triangle Trigonometry

Advanced Precalculus Notes 7.1 Right
Triangle Trigonometry; Applications
http://id.mind.net/~zona/mmts/trigonometryReal
ms/introduction/rightTriangle/trigRightTriangle.h
tml
The website above provides an interesting
demonstration on trig calculations for several
angles.
Finding the Value of Trig functions from a right
triangle:
Constructing a Rain gutter
A rain gutter is to be constructed of aluminum sheets 12
inches wide. After marking off a length of 4 inches from each edge,
this length is bent up at an angle  .
express the area A of the opening as a function of  .
Graph A = A(  ) and find the angle  which makes A largest.
Cofunctions of complementary angles are congruent:
sin   cos(

2
 )
Solve the right triangles:
mB  40
a2
mC 
mA 
b
c
a3
b2
mA 
mB 
mC 
c
Using a transit, a surveyor took a sighting at a rock across the river,
then turned 90° and walked 200 meters. Using the transit, he again
sighted the rock at a 20° angle from the path that he walked. What
is the width of the river, rounded to the nearest meter?
A straight trail leads from the Alpine Hotel, elevation 8000 feet, to
a scenic overlook, at 11,100 feet elevation. The length of the trail is
14,100 feet. What is the inclination (grade) of the trail?
The Model 8339 Laser Ceilometer measures cloud height up to
30,000 feet by calculating the return time of laser light pulses
reflected by the cloud base. Using the ceilometer on a base (distance
from the light to the receiver) of 300 feet, it was determined that the
angle of elevation of the light detector was 75°. What is the height of
the cloud cover?
Two observations are taken 400 feet from a flagpole. The angle of
elevation to the top of the flag is 56.5° and the angle of elevation to
the bottom of the flag is 55.1°. How tall (wide) is the flag?
Assignment: page 527: 1 –
9, 15, 16, 18, 19, 21, 23,
29, 39, 43, 49, 51, 59