Question

express sin g as a fraction in simplest terms.
answer
attempt 1 out of 2
sin g =

Explanation:

Step1: Find the length of \(HI\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let \(a = HI\), \(b = HG = 36\), \(c = IG=45\). Then \(HI=\sqrt{45^{2}-36^{2}}=\sqrt{(45 + 36)(45 - 36)}=\sqrt{81\times9}=\sqrt{729}=27\).

Step2: Use the sine formula

The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle G\), the opposite side is \(HI = 27\) and the hypotenuse is \(IG = 45\). So \(\sin G=\frac{HI}{IG}=\frac{27}{45}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 27 and 45 is 9. \(\frac{27\div9}{45\div9}=\frac{3}{5}\).

Answer:

\(\sin G=\frac{3}{5}\)