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

Find The Sin Of Write Your Answer As An Integer Or A Decimal Rounded To The Nearest Hundredth class=

Sagot :

Answer:

[tex]sin(G)=0.91[/tex]

Step-by-step explanation:

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

[tex]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}[/tex]

Thus, [tex]sin(G)=\frac{\sqrt{70}}{\sqrt{85}}\approx0.91[/tex]
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
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