In a triangle ABC- if -AB-7- -BC-5 and -CA-3- if the projection of BC on CA is equal to n-2- then the value of n is

Finding the projection of BC on CA and the value of nGiven the sides of a triangle are,|AB|=a=7|BC|=b=5|CA|=c=3The figure is as shown:Projection of BC on CA=BCc ...

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Byju's Answer

Standard VII

Mathematics

Properties of Isosceles and Equilateral Triangles

In a triangle...

Question

In a triangle $A B C$ , if $|\vec{A B}| = 7$ , $|\vec{B C}| = 5$ and $|\vec{C A}| = 3$ , if the projection of $\vec{B C}$ on $\vec{C A}$ is equal to $\frac{n}{2}$ , then the value of $n$ is

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Solution

Finding the projection of $\vec{B C}$ on $\vec{C A}$ and the value of $n$
Given the sides of a triangle are,
$|\vec{A B}| = a = 7$
$|\vec{B C}| = b = 5$
$|\vec{C A}| = c = 3$
The figure is as shown:
Projection of $\vec{B C}$ on $\vec{C A}$ $= B C \cos (θ)$ , which implies that,
$|C M| = |B C| \cos (θ) = |B C| |\frac{b^{2} + c^{2} - a^{2}}{2 b c}| = 5 |\frac{25 + 9 - 49}{30}| = 5 |\frac{34 - 49}{30}| = 5 |\frac{- 15}{30}| = \frac{5}{2}$
Comparing this with $\frac{n}{2}$ , we get, $n = 5$
Therefore, the value of $n$ is equal to $5$ .

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In a triangle ABC, if AB→=7, BC→=5 and CA→=3, if the projection of BC→ on CA→ is equal to n2, then the value of n is

In a triangle $A B C$ , if $|\vec{A B}| = 7$ , $|\vec{B C}| = 5$ and $|\vec{C A}| = 3$ , if the projection of $\vec{B C}$ on $\vec{C A}$ is equal to $\frac{n}{2}$ , then the value of $n$ is