Question

50 points. Please explain each step​

Answer 1

sin theta = 3 sqrt(21)/17

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)=(3√(21))/(17)`

Solution given:

Cos
`\theta_(1)=(10)/(17)`

`(adjacent)/(hypotenuse)=(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

`√(x²)=√(189)`

x=
`3√(21)`

now

In I Quadrant sin angle is positive

Sin
`\theta_(1)=(perpendicular)/(hypotenuse)`

Sin
`\theta_(1)=(3√(21))/(17)`