Question

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

2. (NOT A MULTIPLE CHOICE)
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 degrees with the ground.

a. How high is the kite?


b. How far away is the kite horizontally?

Answer 1

1. 10°

2.

a) 79.9 or 80 m

b) 159.8 meters or 160 m

Step-by-step explanation:

1.

wheelchair camp is hypotenuse,

height is opposite.

by using sine rule we can find angle of inclination.

Sin θ= opposite/hypotenuse =0.7/4.2

θ= Sin inverse( 0.7/4.2)

θ = 9.59 degrees (to the nearest degree)

Therefore, the angle of inclination of the wheelchair ramp to the nearest degree is 10 degrees.

2.

a. Let's call the height of the kite h. From the information given, we know that the length of the string, which is the hypotenuse of a right triangle, is 176 m, and the angle between the string and the ground is 27 degrees. We can use the sine function to solve for the height:

sin 27° = opposite/hypotenuse = h/176

h = sin 27° x 176 = 79.9m (rounded to one decimal place)

Therefore, the kite is about 79.9 meters above the ground.

b. To find the horizontal distance between the kite and the person on the ground, we can use the cosine function. Again, the hypotenuse is 176 m, and the angle between the string and the ground is 27 degrees. Let's call the horizontal distance d:

cos 27° = adjacent/hypotenuse = d/176

d = cos 27° x 176 = 159.8 m (rounded to one decimal place)

Therefore, the kite is about 159.8 meters away from the person horizontally.

Answer 2

Answers in bold.

• 1. angle of inclination = 10 degrees
• 2a. Height = 80 meters
• 2b. Horizontal distance = 157 meters

Each result is approximate, and rounded to the nearest whole number. If the rounding instructions for problem 2 are different (say to the nearest tenth), then be sure to follow those instructions. The diagrams are provided below.

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Step-by-step explanation:

Problem 1

Draw a right triangle with vertical leg 0.7 meters and hypotenuse 4.2 meters. Refer to figure 1 shown below. The angle theta (symbol
`\theta`) is opposite the vertical side. It's the angle of inclination, aka angle of elevation.

sin(angle) = opposite/hypotenuse

sin(theta) = 0.7/4.2

sin(theta) = 7/42

sin(theta) = 1/6

theta = arcsin(1/6)

theta = 9.594068 approximately

theta = 10 degrees approximately

Make sure your calculator is in degree mode. The notation arcsin, aka arcsine, is the same as inverse sine. It has the notation
`\sin^(-1)` on many calculators.

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Problem 2a

Refer to figure 2 shown below.

sin(angle) = opposite/hypotenuse

sin(27) = y/176

y = 176*sin(27)

y = 79.9023279541602

y = 80 meters

The kite is about 80 meters off the ground.

Side note: 80 meters = 262.467 feet approximately

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Problem 2b

Refer to figure 2 shown below.

cos(angle) = adjacent/hypotenuse

cos(27) = x/176

x = 176*cos(27)

x = 156.817148257152

x = 157 meters

The kite is horizontally about 157 meters away from the person.

157 meters = 515.092 feet approximately

An alternate approach to finding x is through the pythagorean theorem. This requires section 2a done first.

a^2+b^2 = c^2

x^2+y^2 = 176^2

x = sqrt(176^2-y^2)

x = sqrt(176^2-79.9023279541602^2)

x = 156.817148257152

x = 157 meters

Notice we used the value of y, which was computed in section 2a. This means the pythagorean theorem option is not available for section 2a because we don't have enough info about the sides.

Once we know two sides of a right triangle, we can use the pythagorean theorem. In other words, if you did section 2b first, then you could use the pythagorean theorem for section 2a.