help with trigonomretry word problems...please explain how you solved it thanks?

Question

I understand how to solve the formulas and all but im not sure how to draw the diagrams correctly...

At a point 40 feet from the foot of an oak tree, the angle of elevation to the top of the tree is 42 degrees. Find the height of the tree to the nearest foot.

In Rochester parking garage, the levels are 23 feet apart. Each up-ramp to the next level is 144 feet long. Find the measure of the angle of elevation of the incline for each ramp to the nearest tenth of a degree.

Wire braces are needed for the 80-foot-ridge-pole of a circus tent. Each brace is supposed to make a 60 degrees angle with the ground. Fine to the nearest foot, how long each brace should be..

please explain thanks

Answer 1

Use the definition of tangent.
tan(theta) = y / x.
Then
y = x * tan(theta)
You're given x and theta, so just punch them in to your calculator.

Answer 2

T
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P _______________________|F

Look the diagram
T= Top of tree, F=Foot of tree and P= the Point
PF=40 ft and Angle PTF=42
We are interested in FT( the height)
From angle PTF, we want the opposite side(FT) and we have the Adj side(PF). Thus we will use tan(PTF)=FT/PF
tan42=FT/40
FT =36( nearest foot)

The other 2 questions are practically the same.
In No.2, we have the opposite(23) side and the adj(144). Thus
tanX= 23/144
X=9.1 degree

In No.3, we have the opposite(80) side and the angle(60).Thus
tan60=80/y
y=46 foot

It is simple to get started. Just remember the angle given or wanted is fixed. So you look at what side(s) you have and/or what side(s) you want.

For example, you want the Opp and you have the hypo. Then you will use sine since sine is opp over hypo.

So just determine what are the Opp, Adj and Hypo sides from the point of view of the given/wanted angle. Then decide which are the 2 sides to be used for the trigo ratio.

Answer 3

For the first one picture a the tree and the 40 ft is the ground so imagine ur self 40 ft from the tree's foot and an imaginary line rising from ur feet to the top of the tree. You are solving for the angle's opposite. You already have the adjacent. Next one dont one urself cus i dont kno. The last one isn't hard to picture. The pole rises above and is 80 feet high. You are standing some distance away from it and from where u stand a brace/wire stretches to the top of that very pole. You are solving for the hypotenuse. You already have the angle and its opposite. The answers are below.....







1) 36.016
3) 92.376

Answer 4

This phase will be your best friend with trigometry:

SOH CAH TOA
S=sin C=cos T=tan O=opposite A=adjacent H=hypotenuse

1) Draw a tree (vertical line) and from the bottom of it draw a horizontal line. Angle of elevation is going up so you know its from the ground to the top of the tree.

From the angle you have a known adjacent line and you want to fine the opposite line. Angle, adjacent line and opposite line gives you tan. tan(theta) = y/x

Plug and chug

2) Draw a horizontal line acting as the level and a hypotenuse as the ramp. Having the hypotenuse and vertical or y line as well as looking for the angle opposite of the vertical line tells you that you need to use sin. sin(theta)=y/h

3) Draw your figure. You have the pole or y line length and the angle opposite of it. You are looking for the adjacent line which says you need to use tan. Same as #1


Hope that helps.

Answer 5

These are all right triangle problems that use tangent, sine, and cosine formulas.

1.
tan α = (side opp)/(side adjacent)
tan 42 = (side opp)/40
side opp = 0.9 * 40 = 36 ft

2
sin α = (side opposite)/hypotenuse
sin x = 23/144 = 0.15972
x = 9.2 deg

3.
cos α = (side adjacent)/hypotenuse
cos 60 deg = 80/x
0.5 = 80/x
x = 160 ft.


.

Answer 6

you desire the LCM (least hassle-free different) of 24 and 32. First, we desire the top factorization of the two numbers 24 = 2³ • 3 32 = 2? The LCM is two? • 3 = ninety six 3 packs of erasers and four packs of pencils