If x = 39, y = 58, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answ
er to the nearest hundredth.
1 answer:
Answer: 1.64 units
Step-by-step explanation:
Given the following :
X = 39°
Y = 58°
AC = 4 units
Using triangle ABC with x = 39° and AC = 4UNITS,
USING THE Pythagoras, the SOHCAHTOA notation:
AC = opposite = 4units
AB = hypotenus
Sinθ = opposite / hypotenus
x = Θ = 39°
Sinx = opposite / hypotenus
Sin39° = 4 / AB
0.6293203 = 4 / AB
AB = (4 ÷ 0.6293203) = 6.3560629 units
Taking triangle ADC, with x = 58° and AC = 4UNITS,
AC = opposite = 4units
AD = hypotenus
Sinθ = opposite / hypotenus
y = Θ = 58°
Sinx = opposite / hypotenus
Sin58° = 4 / AD
0.8480480 = 4 / AD
AD = (4 ÷ 0.8480480) = 4.7167136 units
Difference between AB and AD
(6.3560629 - 4.7167136) = 1.6393493
= 1.64 units
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The shortest distance separating Julio from Sarah is 111.8ft
To know the distance of the shortest bridge between Julio and Sarah, the following procedure must be carried out.
We know that Julio walked 100ft to one side and Sarah walked 20ft to the opposite side, that is, on the <em>y-axis</em> they are 120ft apart.
On the other hand, Julio stayed by the river and Sarah walked 9ft away from the river, that is, on the <em>x-axis</em> they are separated by a distance of 59ft (assuming that the width of the river is 50ft).
To know the linear distance that separates them, it is necessary to use the following formula of the Pythagorean theorem.
c² = a² + b²
c=
From this operation we know the value of a and b:
a = 120ft
b = 59ft
Now we just have to replace the values in the formula.
c =
c =
c =
c = 133,7
However, 133.5ft is not the value of the bridge distance because Sarah went 9ft away form the river. Then a portion must be subtracted from her to calculate the exact portion of the distance above the river.
For this we must calculate the distance that separates them that is above the Earth, for this we use the same mathematical formula.
c =
c =
c =
c = 21,9ft
So the distance a part of the Earth covers is 21.9ft. To find out how far the bridge should be over the river, we subtract 21.9ft from the total distance 133.7ft
133,7ft - 21,9ft = 111,8ft
Note: This question is incomplete because it has missing information (the length and width of the river).
Learn more in: brainly.com/question/25292638
