Answer:
see explanation
Step-by-step explanation:
(1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{0.7}{4.2}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{0.7}{4.2}[/tex] ) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{176}[/tex] ( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{176}[/tex] ( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
Step-by-step explanation:
[tex]1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{0.7}{4.2}4.20.7 , then
x = sin^{-1}sin−1 (\frac{0.7}{4.2}4.20.7 ) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{y}{176}176y ( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = \frac{adjacent}{hypotenuse}hypotenuseadjacent = \frac{x}{176}176x ( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
[/tex]
