word math problems, algebra homework help

I have placed the following questions and their answers and explanations below. Please explain in more detail. Thank you.

Find the tangent of ZE.
D
39
80
E
89
с
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan (E)
You answered:
The tangent (tan) of an angle in a right triangle is a ratio. It is the length of the opposite leg
(opp) divided by the length of the adjacent leg (adj). The opposite leg is the side across from
the specified angle and the adjacent leg is the leg next to the specified angle.
tan(x)
opp
adj
х
Take the formula for the tangent of ZE and plug in the relevant side lengths.
D
39
80
E
89
с
tan (E)
opp
adj
Definition of tangent
CD
DE
Substitute opp = CD and adj – DE
=
80
39
Plug in CD = 80 and DE = 39
So, tan (E)
80
39
x is an acute angle. Find the value of x in degrees.
sin(x) = 0.1
Write your answer as an integer or as a decimal rounded to the nearest hundredth.
o
X =
You answered:
The inverse sine function (sin-) satisfies the following equation if -90° SX s 90°:
sin – [sin(x)]
= X
Use a calculator’s inverse sine function (sin-?) to find x.
sin(x) = 0.1
Given
sin – [sin(x)] = sin 0.1
Take the inverse sine (sin) of both sides
X =
sin? 0.1
Simplify sin” [sin (x)]
x = 5.739170….
Find sin 0.1
X 5.740
Round to the nearest hundredth
So, X 5.740
Find mZI
K
9
1
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m2
You answered:
MZI
The cosine (cos) of an angle in a right triangle is a ratio. It is the length of the adjacent leg
(adj) divided by the length of the hypotenuse (hyp). The adjacent leg is the leg next to the
specified angle and the hypotenuse is the side across from the right angle.
/
Cos(x) – adj
hyp
Find cos (I).
Find the cosine (cos) of mZI.
S
m
]
1
6
COS(I) –
adj
hyp
Definition of cosine
TU
IK
Substitute adj-1) and hyp-IK
Plug in D) – 6 and IK – 9
-0.666666…
Divide
So, cos (I) – 0.666666….
Find m2I.
Use a calculator’s inverse cosine function (cos-1) to find m2I.
cos(I) -0.666666…
Given
cos-1 [cos (I)) – COS-1 0.666666.
Take the inverse cosine (cos) of both sides
MZI – cos-1 0.666666…
Simplify cos(cos(1)
mZI – 48.189685…O
Find cos 0.666666…
To the nearest tenth, mZI 48.2º.