<u>Solution-</u>
As given in △ABC,
As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e
According to the sine law,
In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.
Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.
Case-1. Length of a is 7
As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.
Case-2. Length of b is 7
As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.
Case-3. Length of c is 7
As this is the last case, this must be true.
Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.
Answer:
90 km, N 46° E
Step-by-step explanation:
<em>A jet flies due North for a distance of 50 km and then on a bearing of N 70° E for a further 60 km. Find the distance and bearing of the jet from its starting point.</em>
Look at the diagram I drew of this scenario. You can see the jet flies North for 50 km, and then turns at a 70° angle to fly another 60 km. We want to find the distance from the starting point, SP, to angle C (labeled).
This will be the jet's distance from its starting point.
In order to find the bearing of the jet from its starting point, we will need to find the angle formed between distances b and c, labeled angle A.
The <u>Law of Cosines</u> will allow us to use two known sides and one known angle to solve for the sides opposite of the known angle.
In this case, the known angle is 110° (angle B) so we will use the <u>Law of Cosines</u> respective to B.
Substitute the known values into the equation and solve for b, the distance from the starting point (A) to the endpoint (C).
- b² = (60)² + (50)² - 2(60)(50) cos(110°)
- b² = 6100 -(-2052.12086)
- b² = 8152.12086
- b = 90.28909602
- b ≈ 90 km
The distance of the jet from its starting point is 90 km. Now we can use this b value in order to calculate angle A, the bearing of the jet.
The <u>Law of Cosines</u> with respect to A:
Substitute the known values into the equation and solve for A, the bearing from the starting point (clockwise of North).
- (60)² = (90.28909602)² + (50)² - 2(90.28909602)(50) cosA
- 3600 = 8152.12086 - 6528.909602 cosA
- -4552.12086 = -6528.909602 cosA
- 0.6972252853 = cosA
- A = cos⁻¹(0.6972252853)
- A = 45.79519
- A ≈ 46°
The bearing of the jet from its starting point is N 46° E. This means that it is facing northeast at an angle of 46° clockwise from the North.
This is the standard form equation 
What is the ellipse?
The equation for an ellipse is typically written as x² a² + y² b² = 1. x² a² + y² b² = 1. An ellipse with its origin at the center is defined by this equation. The ellipse is stretched further in both the horizontal and vertical directions if a > b, a > b, and if b > a, b > a, respectively.
The standard form of the equation of an ellipse with center (h, k)and major axis parallel to the x-axis is:
where,
a > b
the length of the major axis is 2a
the coordinates of the vertices are (h±a,k)
the length of the minor axis is 2b
the coordinates of the co-vertices are (h,k±b)
the coordinates of the foci are (h±c,k),
where c² = a² − b².
so,
Hence, this is the standard form equation .
To learn more about ellipse, visit
brainly.com/question/16904744
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Answer:
To my knowledge of congruency, I would say the answer is A,
Step-by-step explanation:
Hope this helped!!!
