I am taking trigonometry and I am a retard (kinda) i need help with these 3 questions

Question

1------A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.?

2------Use the fact that the trigonometric functions are periodic to find the exact value of the expression.

sin 10pi / 3

3..........Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression.

If tan(2nd power) θ = 3, find the exact value of sec (2nd Power) θ.

Answer 1

(1)

Length of ladder is 25 ft

Let height of the wall is x 

From the above figure sin Ø = opposite / hypotenuse

sin 41.5° =  x / 25

0.6626 =  x / 25

 x / 25 = 0.6626

x = 0.6626 * 25 

x = 16.56

So height of the wall is 16.56 ft

Answer 2

(2)

sin 10π/ 3

10π/3 = 9π/3 + π/3

           =3π +  π/3

As  trigonometric functions are periodic 2π + Ø = Ø

10π/3 = 3π +  π/3

           = 2π +( π + π/3 )

           = π + π/3

sin (π + π/3) = - sin π/3

                     = -√3/2

So  sin(10π/ 3) = -√3/2

Answer 3

(3)

From trigonometric Identities we know that  sec² ø = 1 + tan² ø

Given tan² ø = 3

sec² ø = 1+ 3²

          = 1+ 9

          = 10

So sec² ø = 10