Q). A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 40 m, the angle of elevation changes to 45°. Find the height of the building correct to the nearest metre.
Answers
Answer :-
\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}
↦Firstlylet
′
sunderstandtheconceptused
Here the concept of Quadratic Equations has been used. According to this, the value of variable in the equation has two values. These values are the coordinates of the points of intersection of x - axis. Using thos concept, let's do it !!
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★ Question :-
Determine the quadratic equation given the sun of the roots -3 and product of the roots 7.
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★ Solution :-
Given,
» Sum of the roots = -3
» Product of the roots = 7
• Let the required quadratic equation be
ax² + bx + c = 0
Here coefficient of x² = a, x = b and c is the constant term.
So its roots will be α and β.
We know that,
\: \: \large{\boxed{\rm{\leadsto \: \: \alpha \: + \beta \: = \: \dfrac{(-b)}{a}}}}
⇝α+β=
a
(−b)
\: \: \large{\boxed{\rm{\leadsto \: \: \alpha \: \times \: \beta \: = \: \dfrac{c}{a}}}}
⇝α×β=
a
c
Then, according to the question, :-
~ Case I :-
⌬ α + β = -3
\: \: \large{\rm{\longmapsto \: \: \dfrac{(-b)}{a} \: = \: \dfrac{(-3)}{1}}}⟼
a
(−b)
=
1
(−3)
On comparing, LHS and RHS, we get,
⌬ (-b) = (-3) and (a) = 1
Then,
\: \: \large{\boxed{\boxed{\bf{a \: = \: 1 \: , \: b \: = \: 3}}}}
a=1,b=3
~ Case II :-
⌬ αβ = 7
\: \: \large{\rm{\longmapsto \: \: \dfrac{c}{a} \: = \: \dfrac{7}{1}}}⟼
a
c
=
1
7
On comparing, LHS and RHS, we get,
⌬ c = 7 and a = 1
\: \: \large{\boxed{\boxed{\bf{c \: = \: 7}}}}
c=7
So,
⌬ a = 1
⌬ b = 3
⌬ c = 7
Now by applying these values, in the quadratic equation we get,
⌬ x² + 3x + 7 = 0
So the correct option is Option B.) x² + 3x + 7 = 0
\: \: \overbrace{\underbrace{\boxed{\sf{Hence, \: the \: required \: quadratic \: equation \: is \: \bf{x^{2} \: + \: 3x \: + \: 7 \: = \: 0}}}}}
Hence,therequiredquadraticequationisx
2
+3x+7=0
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\large{\underline{\underline{\implies{Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}}
⟹Confused?Don
′
tworrylet
′
sverifyit:−
For verification, we can simply apply the values we got into the Equation and check is linearity.
We know, that when we apply the value of roots, the sum should come to be 0. Then,
=> ax² + bx + c = 0
=> x² + 3x + 7 = 0
Let the value of x be k, then
=> k² + 3k + 7 = 0
Here the linearity satisfies, since we get the same value after applying the K (constant). So our answer is correct.
Hence, Verified.
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\large{\underbrace{\tt{\leadsto \: \: Reference \: as \: Supplementary \: Counsel \: :-}}}
40°
47°
78m
30°⇝ReferenceasSupplementaryCounsel:−
• Quadratic Equations are the equations which has highest degree of variable to 2 and gives two solutions of the equations. It intersects the graph at x - axis twice.
• Different types of Polynomials are :-
Linear Polynomial - Gives single solution and intersects x - axis just once. Example : Linear Equations
Quadratic Polynomial - Gives two solutions.
Cubic Polynomial - Gives three solutions and intersects x - axis thrice.
Bi - Quadratic Polynomial - Gives four solutions and intersects x - axis four time