The tailgate of the truck is 3 feet above the ground. The incline of a ramp used for loading the truck is 15° find the nearest t
enth of a foot, the length of the ramp
1 answer:
Answer:
11.2 feet
Step-by-step explanation:
Draw a triangle to represent the problem. (See the one attached.)
The sides involved in this problem are the opposite and adjacent to the given angle, so we need to use the tangent ratio.
To find the length of the ramp, we need to find the tangent of angle 15.
tanx = opp/adj
tan15 = 3/x
Multiply by x on both sides:
x(tan15) = (3/x)x
x(tan15) = 3
Divide by tan15 on both sides:
x(tan15) = 3
/tan15 /tan15
x = 3/tan15
Divide tan15 from 3 using a calculator:
x ≈ 11.2
You might be interested in
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
<em></em>
Therefore, the angle between their paths is <em>100.8°</em>
