a. sinB = 9/20.
B = 27o.
b. CosB = h/20.
Cos27 = h/20.
h = ?
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°)
2 answers
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
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
9 answers