Question

1. intro to soh - cah - toa day 2 due: december 14 at 8:00 pm grade: 50% hypotenuse identifying trig ratios (diagram), level 1 identifying trig ratios (diagram), level 1 identifying trig ratios (diagram), level 2 identifying trig ratios (diagram) identifying trig ratios (no diagram) scientific calculator question find the value of sin i rounded to the nearest hundredth, if necessary. sin i = answer attempt 1 out of 2

Explanation:

Step1: Recall sine - ratio formula

The sine of an angle in a right - triangle is given by $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $I$, the side opposite to angle $I$ has length $9$ and the hypotenuse has length $\sqrt{70}$.

Step2: Calculate $\sin I$

$\sin I=\frac{9}{\sqrt{70}}$. Rationalize the denominator: $\sin I=\frac{9}{\sqrt{70}}\times\frac{\sqrt{70}}{\sqrt{70}}=\frac{9\sqrt{70}}{70}\approx\frac{9\times8.367}{70}=\frac{75.303}{70}\approx1.08$. But this is incorrect as we made a mistake above. The hypotenuse should be calculated using the Pythagorean theorem. Let the sides of the right - triangle be $a = 1$, $b = 9$. Then the hypotenuse $c=\sqrt{1^{2}+9^{2}}=\sqrt{1 + 81}=\sqrt{82}$.

Step3: Re - calculate $\sin I$

$\sin I=\frac{9}{\sqrt{82}}$. Rationalize the denominator: $\sin I=\frac{9}{\sqrt{82}}\times\frac{\sqrt{82}}{\sqrt{82}}=\frac{9\sqrt{82}}{82}\approx\frac{9\times9.055}{82}=\frac{81.495}{82}\approx0.99$.

Answer:

$0.99$