Question

what is the value of tan q if sin q 4/5​

Answer 1

Answer:-

Given:-

• sin q = 4/5

to find:-

• The value of tan q

Solution:-

Here,

sin ∅ = opposite/hypotenuse

given,

sin q 4/5

In ΔPQR,

PQ = 5

PR = 4

QR = x

PQ = hypotenuse

PR = opposite

QR = adjacent

Then,

(opposite)² + (adjacent)² = (hypotenuse)²

⇒(4)² + (x)² = (5)²

⇒16 + x² = 25

⇒x² = 25 - 16

⇒x² = 9

⇒x = √9

⇒x = 3

So, adjacent = 3

Then,

tan ∅ = opposite/adjacent

opposite = 4

adjacent = 3

tan q = 4/3

Therefore, the value of "tan q = 4/3"

Answer 2

$\bigstar \sf \large \underline{ \underline{Given :-}}$

• Sin q = 4/5 .

$\bigstar \sf \large\underline{ \underline{To \: find :- }}$

• Value of tan q.

$\bigstar \sf \large \underline{ \underline{Solution :- }}$

We know :

$\mapsto \sf sin (\theta) = opposite \div hypotenuse \\ \\ \mapsto \sf \tan( \theta) = adjecent \div opposite$

Given, Sin q = 4/5 .

So,

Opposite side = 4

Hypotenuse = 5.

We know need to find the adjacent side.

By pythagoras theorem ,

---------------------------------------------

❥︎(Opp)^2+(Adj)^2=Hypotenuse

----------------------------------------------

Acc to question :

Let 'a' be the adjacent side.

$\sf \implies {4}^{2} + {a}^{2} = {5}^{2} \\ \\ \implies \sf \: 16 + {a}^{2} = 25 \\ \\ \implies \sf \: {a}^{2} = 9 \\ \\ \sf \implies \bf \underline{a= 3.}$

Therefore, Adjacent side = 3.

Now, The value of Tan q is ,

» Tan q = Opposite / Adjacent = 4/3

$\mapsto \orange{ \boxed{ \sf \: tan \: q = \frac{4}{3} }}$

Hence, the value of tan q is 4/3 .

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HOPE IT HELPS !