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In right triangle ABC, ∠A is a right angle and sinC=35. What is the ratio for tanC? Enter your answer as the fraction, in simplest terms, like this: 42/53 (Look at the attached image)

In right triangle ABC A is a right angle and sinC35 What is the ratio for tanC Enter your answer as the fraction in simplest terms like this 4253 Look at the at class=

Respuesta :

Answer:

tan(C) = 3/4

Step-by-step explanation:

If the sine of angle C is 3/5 and we want to find the tangent of the angle C, we can first find the cosine of angle C using the following equation:

[tex]sin^2(C) + cos^2(C) = 1[/tex]

[tex](3/5)^2 + cos^2(C) = 1[/tex]

[tex]cos^2(C) = 1 - 9/25[/tex]

[tex]cos^2(C) = 16/25[/tex]

[tex]cos(C) = 4/5[/tex]

Then, we can find the tangent relation using the equation:

[tex]tan(C) = sin(C) / cos(C)[/tex]

[tex]tan(C) = (3/5) / (4/5)[/tex]

[tex]tan(C) = 3/4[/tex]

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