Explain how trigonometry is used in building construction, algebra homework help

Use the information on

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to explain how trigonometry is used in building construction. Include an explanation as to why the ratio of vertical rise to horizontal run on an entrance ramp is the tangent of the angle the ramp makes with the horizontal.

13-1
Right Triangle Trigonometry
angle A
GET READY for the Lesson
The Americans with Disabilities
Act (ADA) provides regulations
designed to make public buildings
accessible to all. Under this act,
the slope of an entrance ramp
designed for those with mobility
disabilities must not exceed a ratio
of 1 to 12. This means that for
every 12 units of horizontal run,
the ramp can rise or fall no more than 1 unit
When viewed from the side, a ramp forms a right triangle. The slope
of the ramp can be described by the tangent of the angle the ramp
makes with the ground. In this example, the tangent of angle A is a
11
Main Ideas
. Find values of
trigonometric functions
for acute andes
. Solve problems
involving right triangles.
New Vocabulary
trigonometry
trigonometric functions
sine
cosine
tangent
cosecant
secant
cotangent
solve a right triangle
angle of elevation
angle of depression
12 L
B
opposite
leg
Reading Math
Trigonometry
The word trigonometry is
derived from two Greek
words trigon meaning
triangle and metra meaning
measurement
Trigonometric Values The tangent of an angle
is one of the ratios used in trigonometry
Trigonometry is the study of the relationships
among the angles and sides of a right triangle. hypotenuse
Consider right triangle ABC in which the
measure of acute angle A is identified by the
Greek letter theta, a. The sides of the triangle
are the hypotenuse, the icy opposite, and the
leg adjacent to 6.
Using these sides, you can define six trigonometric functions: sine,
cosine, tangent, cosecant, secant, and cotangent. These functions are
abbreviated sin, cos, tan, csc, sec, and cot, respectively.
A
adjacent lop
C
KEY CONCEPT
Trigonometric Functions
If & is the measure of an acute angle of a right triangle, opp is the measure
of the leg opposite e, adj is the measure of the leg adjacent to , and hyp is
the measure of the hypotenuse, then the following are true.
sin
opp
COS
opp
tan-
hyp
adi
hyp
CSC
hyp
seca
opp
adi
cot
adi
opp
Notice that the sine, cosine, and tangent functions are reciprocals of the
cosecant, secant, and cotangent functions, respectively. Thus, the following
are also true.
hyp
CSC
sec
cot
sino
cos
tan
Lesson 13-1 Right Triangle Trigonometry 759