Question

A ladder 20 m long rest against a vertical wall so that the foot of the ladder is 9 m from the wall
a. Find, correct to the nearest degree, the angle that the ladder makes with the wall
b. Find, correct to 1 decimal place, the height above the ground at which the upper end of the ladder touches the wall
Pls answer with workings I need it very urgent

Solve the following equation
2. sin y = cos ( y +20°)

Answer 1

a. sinB = 9/20.
B = 27o.

b. CosB = h/20.
Cos27 = h/20.
h = ?

Answer 2

1.

a.

cos θ = 9 / 20 = 0.18

θ = cos⁻¹ ( 0.18 ) = 79.630240195°

θ = 80° θ to the nearest degree

b.

Pythagorean theorem

h = √ ( 20² - 9² ) = √ ( 400 - 81 ) = √ 319 = 17.8605711

h = 17.9 m correct to 1 decimal place

2.

sin y = cos ( y + 20° )

Use identity:

cos ( y ) = sin ( 90° - y )

sin y = sin [ 90° - ( y + 20° ) ]

sin y = sin ( 90° - y - 20° )

sin y = sin ( 70° - y )

sine is equal so:

y = 70° - y

Add y to both sides

y + y = 70° - y + y

2 y = 70°

y = 70° / 2

y = 35°

sin ( 180° - θ ) = sin θ

so

sin ( 180° - 35° ) = sin 35°

sin 145° = sin 35°

Period of sine = 360°

So, the solutions are:

y = 35° ± n ∙ 360°

and

y = 145° ± n ∙ 360°

where

n = some integer