Question

50 points. Please explain each step​

Answer 1

Answer:

sin theta = 3 sqrt(21)/17

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp by using the Pythagorean theorem

adj^2 + opp ^2 = hyp^2

10^2 +opp^2 = 17^2

100 + opp^2 = 289

opp^2 = 289-100

opp^2 = 189

Taking the square root

opp = sqrt(189)

opp = 3 sqrt(21)

Since we are in the first quad, opp is positive

sin theta = opp /hyp

sin theta = 3 sqrt(21)/17

Answer 2

Sin$\theta_{1}=\frac{3\sqrt{21}}{17}$

Solution given:

Cos$\theta_{1}=\frac{10}{17}$

$\frac{adjacent}{hypotenuse}=\frac{10}{17}$

equating corresponding value

we get

adjacent=10

hypotenuse=17

perpendicular=x

now

by using Pythagoras law

Hypotenuse ²=perpendicular²+adjacent ²

substituting value

17²=x²+10²

17²-10²=x²

x²=17²-10²

x²=189

doing square root

$\sqrt{x²}=\sqrt{189}$

x=$3\sqrt{21}$

now

In I Quadrant sin angle is positive

Sin$\theta_{1}=\frac{perpendicular}{hypotenuse}$

Sin$\theta_{1}=\frac{3\sqrt{21}}{17}$