Answer:

Step-by-step explanation:
Hope it will help you.
The absolute value of 8 that is |8| is equal to 8.
We have given that,
|8|
We have to determine the value of |8|.
<h3>What is the absolute value?</h3>
The absolute value or modulus of a real number x denoted |x|, is the non-negative value of x without regard to its sign. Namely,
if x is a positive number, and
if x is negative, and
.
Absolute values only find the true distance of a number from 0. Distance is always positive, so the absolute value of anything is always positive.
|8| = 8
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By using trigonometric relations, we will see that x = 9.97°.
<h3>
How to find the missing angle?</h3>
First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus).
Where:
- θ = 26°
- Adjacent cathetus = k
- Opposite cathetus = 55ft.
Replacing that we get:
Tan(26°) = 50ft/k
Solving this for k, we get:
k = 55ft/tan(26°) = 112.8 ft
Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:
- angle = x
- opposite cathetus = 55ft
- adjacent cathetus = 112.8ft + 200ft = 312.8ft.
Then we have:
Tan(x) = (55ft/312.8ft)
Using the inverse tangent function in both sides, we get:
x = Atan(55ft/312.8ft) = 9.97°
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