In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=71°, and JH = 2 feet. Find the length of IJ to the nearest tenth of a foot.
1 answer:
Answer:
IJ is 5.8 ft
Step-by-step explanation:
Here, we want to calculate the length of IJ
to Find IJ, we need the appropriate trigonometric ratio
The trigonometric ratio to use in this case is the one that connects the opposite and the adjacent
from the question, IJ is the opposite
This is the side facing the given angle
HI is the hypotenuse which is the side facing the right-angle
HJ is the third side which is the adjacent
Mathematically;
That is the Tan
Tan 71 = IJ/2
IJ = 2 Tan 71
IJ = 5.8
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The range of the equation is
Explanation:
The given equation is
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<u>Range:</u>
The range of the function is the set of all dependent y - values for which the function is well defined.
Let us simplify the equation.
Thus, we have;
This can be written as
Now, we shall determine the range.
Let us interchange the variables x and y.
Thus, we have;
Solving for y, we get;
Applying the log rule, if f(x) = g(x) then , then, we get;
Simplifying, we get;
Dividing both sides by , we have;
Subtracting 7 from both sides of the equation, we have;
Dividing both sides by 2, we get;
Let us find the positive values for logs.
Thus, we have,;
The function domain is
By combining the intervals, the range becomes
Hence, the range of the equation is