Please show the work.

1. A wheelchair ramp is 4.2 m long. I rises 0.7 . What is its angle of inclination to the nearest degree?

2. A person flying a kite has released 176 m of string and attached the end to the ground. The string makes an angle of 27 degree with the ground. How high is the kite? How far away is the kite horizontally? Answer to the nearest meter.

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

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