Question

Find the sin of Write your answer as an integer or a decimal rounded to the nearest hundredth.

Answer 1

Answer:

$sin(G)=0.91$

Step-by-step explanation:

Recall that $sin(\theta)=\frac{opposite}{hypotenuse}$ with respect to the angle $\theta$ for a right triangle. Since we are given our hypotenuse of $\sqrt{85}$ and our adjacent side of $\sqrt{15}$, we can use the Pythagorean Theorem to solve for the missing opposite side:

$a^2+b^2=c^2\\\\(opposite)^2+(adjacent)^2=(hypotenuse)^2\\\\(opposite)^2+(\sqrt{15})^2=(\sqrt{85})^2\\\\(opposite)^2+15=85\\\\(opposite)^2=70\\\\opposite=\sqrt{70}$

Thus, $sin(G)=\frac{\sqrt{70}}{\sqrt{85}}\approx0.91$

Answer 2

Using Pythagorean theorem FH is equal to √70(radical) therefore sine of G would be equal to sin^-1(√70/√85)=65.16010754 rounded to the hundredths place is 65.16