Jane is using a carpenter’s square at eye level to determine the height of the tree, as shown in the figure. She is standing 9 f
eet from the tree and her eye level is 5.2 feet above the ground.
Which measurement is closest to the height of the tree in feet?
Which measurement is closest to the height of the tree in feet?
1 answer:
Applying the trigonometry ratio, TOA, the measurement that is closest to the height of the tree in feet is: D. 21
Recall:
Trigonometry ratios can be applied to solve any right triangle for missing side lengths or angles. They are denoted with the acronym, SOH CAH TOA.
Using trigonometry ratio, TOA, find the length of the side of the tree in the bigger triangle as follows:
tan 60 = x/9
x = tan 60 × 9
x = 15.6 ft
Height of the tree = 15.6 + 5.2 = 20.8 ft.
- In conclusion, applying the trigonometry ratio, TOA, the measurement that is closest to the height of the tree in feet is: D. 21
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Answer:
(x, y) = (4, -3)
Step-by-step explanation:
- x-3y=13
- 2x+4y=-4
First of all, look at the given equations. Here, we see that the second equation has coefficients that all have a factor of 2. If we divide that out, we get an equation that has an x-coefficient of 1, matching the x-coefficient in the first equation.
Here is the reduced second equation:
x +2y = -2
Now, if we subtract one equation from the other, the variable x will be eliminated. We want to choose that subtraction wisely.
We note that the y-coefficient in the first equation is less than that in the second equation. If we subtract the first equation from the second, the result will have a positive y-coefficient:
(x +2y) -(x -3y) = (-2) -(13)
5y = -15 . . . . . . . . . . . . . . . . simplify. Note that the x-variable is eliminated, which is the purpose of this exercise.
y = -3 . . . . . . . divide by 5
We can use this value in the reduced second equation to find the value of x:
x +2(-3) = -2
x = 4 . . . . . . . . . add 6 and simplify
The solution is (x, y) = (4, -3).
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I find a graphing calculator provides an easy and reliable check of the answer.
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<em>Comment on linear combination</em>
This method is often called "elimination," because the purpose of combining the equations in a particular way is to eliminate one of the variables. This requires you look at the coefficients of the variables and devise a plan to combine them so the resulting coefficient for one of the variables is zero.
In the worst case, you can combine ...
- ax +by = c
- dx +ey = f
by multiplying the second equation by <em>a</em> and the first by <em>-d</em>:
a(dx +ey) -d(ax +by) = a( f) -d(c)
y(ae -bd) = fa -cd . . . . . . simplify; x is eliminated
This sort of approach results in a formula for the solution known as Cramer's Rule.
y = (fa-cd)/(ae-bd)
The corresponding solution for x is ...
x = (ce-bf)/(ae-bd)
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The point of looking at the equations first is that you can often choose which variable to eliminate and what multiplier to use to minimize the amount of arithmetic involved—as we did above.
