Question

Help me please need help​

Answer 1

Answer:

Step-by-step explanation:

Hypotenuse:  The longest side in the triangle and it is opposite to 90°

Opposite Side: The side oppoiste to the angle.

Adjacent side: The side next to the angle.

First find 'c' using Pythagorean theorem,

c² = 9² + 12²

    = 81 + 144

    = 225

c =√225

c = 15

$\sf \ Sin \ \theta = \dfrac{opposite \ side \ of \ \theta}{hypotenuse}= \dfrac{12}{15}$

$\sf \ Cos \ \theta = \dfrac{adjacent \side \ of \ \theta}{hypotenuse}= \dfrac{9}{15}\\\\ Tan \ \theta= \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \ theta}= \dfrac{12}{9}$

$\sf \ Csc \ \theta= \dfrac{hypotenuse}{opposite \ side \ of \ \ theta}= \dfrac{15}{12}\\\\\ Sec \ \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \theta}= \dfrac{15}{9}\\\\Cot \ \theta= \dfrac{adjacent \ side \ of \ \theta}{opposite \ side \ of \ \theta}= \dfrac{9}{12}$

$\sf \ Sin \ \alpha = \dfrac{opposite \ side \ of \ \alpha \theta}{hypotenuse}= \dfrac{9}{15}$

$\sf \ Cos \ \alpha = \dfrac{adjacent \side \ of \ \alpha }{hypotenuse}= \dfrac{12}{15}\\\\ Tan \ \alpha = \dfrac{opposite \ side \ of \ \alpha }{adjacent \ side \ of \ \ theta}= \dfrac{9}{12}$

$\sf \ Csc \ \alpha = \dfrac{hypotenuse}{opposite \ side \ of \ \alpha }= \dfrac{15}{9}\\\\\ Sec \ \alpha \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \alpha }= \dfrac{15}{12}\\\\Cot \ \alpha = \dfrac{adjacent \ side \ of \ \alpha }{opposite \ side \ of \ \alpha }= \dfrac{12}{9}$