Math  /  Trigonometry

QuestionExpress sinX\sin X as a fraction in simplest terms.

Studdy Solution

STEP 1

1. We are given a right triangle with a right angle at Y.
2. The side opposite angle X is known.
3. The hypotenuse of the triangle is known.
4. We need to express sinX\sin X as a fraction in simplest terms.

STEP 2

1. Identify the sides of the triangle relevant to sinX\sin X.
2. Use the definition of sine to express sinX\sin X as a fraction.
3. Simplify the fraction to its simplest terms.

STEP 3

Identify the sides of the triangle relevant to sinX\sin X. In a right triangle, sinX\sin X is the ratio of the length of the side opposite angle X to the length of the hypotenuse.
The side opposite angle X is 24, and the hypotenuse is 26.

STEP 4

Use the definition of sine to express sinX\sin X as a fraction:
sinX=opposite sidehypotenuse=2426\sin X = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{24}{26}

STEP 5

Simplify the fraction 2426\frac{24}{26} to its simplest terms. Find the greatest common divisor (GCD) of 24 and 26, which is 2.
2426=24÷226÷2=1213\frac{24}{26} = \frac{24 \div 2}{26 \div 2} = \frac{12}{13}
Thus, sinX\sin X in simplest terms is:
1213\boxed{\frac{12}{13}}

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