Question

3
If tan 0 =
4
what does sin O = ?

Answer 1

B) 3/5

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Solve

• So, we know that tantheta is 0.75, or 3 quarters, but we have to find the value of sintheta. If there are 4 angles on a triangle, we can label them as BC and AB.

`because~of~the~angles\\BC = 3k\\AB = 4k`

• Now, we must find the value of AC using the pythagoras theorem.

⇒ (AB)² + (BC)² = (AC)²

in which because of AB and BC's values, goes into...

⇒ (4k)² + (3k)² = (AC)²

because of that ↑ you get the values of what is below.

⇒ (AC)² = 16 k² + 9 k²

add 16k and 9k for the result below.

⇒ (AC)² = 25 k²

⇒ AC = ±5k

• Hmm. An angle cannot be negative, so turn 5k to positive 5k. Last but- not least, we have to find the sintheta.

the sin is the side opposite to the angle, so find the hypotenuse and opposite angle.

`Side~opposite~to~angletheta\\= BC(3k)\\\\Hypotenuse\\= AC(5k)`

That said →
`sintheta = (BC)/(AC) = (3k)/(5k) = (3)/(5)`

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