Help with Right Triangles finding length of a side and degrees inside. Sin, Cos, Tan, Phythagorean thm.?

Question

There is the one problem and I have a picture for you to see. This is a huge project for me and everytime I keep doing the sin, cos, tan, I can't seem to get answers that match up. Please help. If you can explain step-by-step how you got it that would be great.

http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=RightTriangle.jpg

Please help! This is due tomorrow!!!

Answer 1

You can find the length of side x by using Pythagorean's theorem
(29.2)^2 +x^2 = (42.6)^2
852.64 +x^2 = 1814.76
x^2 =962.12
x =31.01805926


You can find angle n by
cos(n) = adjacent/hypoteneuse
cos(n) = 29.2/42.6
NOTE-arccos is the inverse function of cos
n = arccos(29.2/42.6) = 46.72930664

The angles of a triangle add up to 180
90 +n +y =180
n +y =90
y = 90-n =90 - 46.72930664 =43.27069336

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You could have also found angle y by doing the following
sin(y) = opposite/hypoteneuse
sin(y) =29.2/42.6
y = arcsin(29.2/42.6) = 43.27069336

Answer 2

first thing i have done is to get the value of x (the side). i got its value by using the pythagorean theorem. this is how it goes:
c^2 = a^2 + b^2 ----------> statement of the pythagorean thm
c = hypotenuse
a = side y (opposite of the angle Y)
b = side n (opposite of the angle N)

(42.6)^2 = (29.2)^2 + b^2
b^2 = (42.6)^2 - (29.2)^2
b^2 = 1,814.76 - 852.64
b^2 = 962.12
get the square root of both sides to have the value of b (side opposite angle N)
b = 31.02 m

now that you have the values of the three sides, it would be easier to get the values of the angles N and Y.

let us first focus on the value of angle Y:
i will use sine, cosine and tangent to find the value of angle Y:

sin Y = opposite side / hypotenuse
sin Y = 29.2 / 42.6
sin Y = 0.6854
Y = arcsin (0.6854)
Y = 43.27 degrees

cos Y = adjacent side / hypotenuse
cos Y = 31.02 (this is the value of x that we have solved awhile ago using pythagorean thm) / 42.6
cos Y = 0.7282
Y = arccos (0.7282)
Y = 43.27 degrees

tan Y = opposite side / adjacent side
tan Y = 29.2 / 31.02
tan Y = 0.9413
Y = arctan (0.9413)
Y = 43.27 degrees

the values for the angle Y are all the same whatever trigonometric function you use.=)

so now we will proceed in looking for the value of angle N.

sin N = opposite side / hypotenuse
sin N = 31.02 / 42.6
sin N = 0.7282
N = arcsin (0.7282)
N = 46.73 degrees

cos N = adjacent side / hypotenuse
cos N = 29.2 / 42.6
cos N = 0.6854
N = arcos (0.6854)
N = 46.73 degrees

tan N = opposite side / adjacent side
tan N = 31.02 / 29.2
tan N = 1.0623
N = arctan (1.0623)
N = 46.73 degrees

Again the values for the angle N are the same whatever trigonometric function we have used.

And if you add the values of the three angles:
90 degrees + 46.73 degrees + 43.27 degrees = 180 degrees

we all know that a triangle should be composed only of angles that have a sum of 180 degrees. Therefore, our answer is correct! Ü

hope I had helped you in your project.

Answer 3

The other two angles do matter, for example, 30:60:90 triangles have sides 1, radical 3, and 2, look for other common pythagorean triples.

Answer 4

n is equal to 90 - y, not 180 - y.

180 = 90 + n + y ----> n + y = 90 ----> n = 90 - y

Use the Pythagorean Theorem to find X. After doing that you will have all the parts needed to find the tangent, sine or cosine of the missing angles. You can then use the arctan, arcsin, or arccos function of your calculator to find the value of one missing angle. Then simply subtract that from 90° to find the other.

X = √(42.6 m)² - (29.2 m)²
X = √1814.76 m² - 852.64 m²
X = √962.12 m²
X ≈ 31.02 m, which I will round down to 31.0 m., since all of your lengths are given only to one decimal place.

Now, since we know X, we can use arctan (31.0 / 29.20) to find n.

n = arctan (31.0 / 29.2) = arctan (1.0616), so n ≈ 46.7°

y = 90° - n
y = 90° - 46.7°
y ≈ 43.3°

Now just substitute the various parts into their proper places to find all the trig functions for each angle.

sin n = 31.0 / 42.6
cos n = 29.2 / 42.6
tan n = 31.0 / 29.2

sin y = 29.2 / 42.6
cos y = 31.0 / 42.6
tan y = 29.2 / 31.0

Answer 5

you can find the length of the missing side by the pythagorean theorem. length of side is equal to the sqrt(42.6^2 - 29.2^2).
The other angles can be found by the law of sines.
sin 90 / 42.6 = sin y / 29.2
and
sin 90/42.6 = sin n/ X and n is equal to 180 - Y.

Answer 6

well law of sines does not work in this case because the sin 90 = 0

just use the regular sine rule

sine = opposite side / hypoteneuse....just use this for both angles after using the pythagorean theorem

Answer 7

The Law of Sines works fine with right triangles.

Answer 8

cos(n) = 29.2/42.6 = 0.68545
n = 46.729°
y = 90 - n = 43.271°
x/42.6 = cos(y) = 0.72812
x = 31.018