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In PQR, Q is a right angle PQ=3,QR=4. If P= and R=, then fi

Question

In $△ PQR, ∠ Q$ is a right angle $PQ = 3, QR = 4$ . If $∠ P = α$ and $∠ R = β$ , then find the values of
$tan β$

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Michael Discussed

△ PQR, ∠ Q

is a right angle

PQ = 3, QR = 4

. If

∠ P = α

and

∠ R = β

, then find the values of

tan β

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given:

PQ = 3, QR = 4

\Rightarrow (PQ)^{2} + (QR)^{2} = (PR)^{2} \Rightarrow (3)^{2} + (4)^{2} = (PR)^{2}

\Rightarrow (PR)^{2} = 25 \Rightarrow PR = 25 = \pm 5

but side

PR

can't be negative so,

PR = 5

tan β

we know that

tan θ = \frac{s i d e o pp os i t e t o an g l e θ}{s i d e a d ja ce n t t o an g l e θ}

here

θ = β

side opposite to angle

β = PQ = 3

sie adjacent to angle

β = QR = 4

so,

tan β = \frac{3}{4}

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Question Text	In $△ PQR, ∠ Q$ is a right angle $PQ = 3, QR = 4$ . If $∠ P = α$ and $∠ R = β$ , then find the values of $tan β$
Answer Type	Text solution:1
Upvotes	150