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nadezda [96]
3 years ago
11

You are building a ramp that must cover a horizontal distance of exactly 17 feet. The angle of the ramp from the ground is 24°.

Determine the length of the ramp, in feet.
Mathematics
1 answer:
tiny-mole [99]3 years ago
6 0

Answer:

Length of the ramp = 18.6 feet (Approx.)

Step-by-step explanation:

Given:

Horizontal distance (base distance) = 17 feet

Angle of elevation = 24°

Find:

Length of the ramp

Computation:

Cosθ = Length of base / Length of hypotenuse

Cos 24 = Horizontal distance (base distance) / Length of the ramp

Cos 24 = 17 / Length of the ramp

0.9135 = 17 / Length of the ramp

Length of the ramp = 17 / 0.9135

Length of the ramp = 18.6 feet (Approx.)

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The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.
Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m  + 40 m  + c = 120 m

61 m +  c = 120 m

c = 120 m - 61 m

c = 59 m

                         B

                     ↓            ↓  

                  ↓                          ↓

                ↓                                       ↓

            A →  →  → →  →  → →  → →    →    →  C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0

Angle B is calculated as follows;

Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0

Angle C is calculated as follows;

Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0

Therefore, the largest angle of the field is 149⁰.

       

8 0
3 years ago
a bar graph shows that sport books received 9 votes. if the scale is 0 to 20 by twos, where should the bar end for the books
leva [86]
If sport books recieved 9 votes then they would be in the middle of 8 and 10 on the bar graph. If you want to know where the bar should end it would be 10.
Hope helps!
6 0
3 years ago
Which of the following pairs of points are both solutions to the equation 2x-5y=6 ? and and and and
zhannawk [14.2K]

Answer:

Any points on the line y=2/5 x - 6/5. See picture below.

Step-by-step explanation:

Convert the equation to slope intercept form and graph it.

2x - 5y = 6

-5y = 6 - 2x

y = -2/-5 x + 6/-5

y=2/5 x - 6/5.

Locate each of the points listed on the graph. If they are a part of the line, then they are solutions.

3 0
3 years ago
six friends share 5 meat pies. each friend first eats half of a meat pie. how much more meat pie does each friend need to eat to
Margaret [11]
So at the beginning, the friends eat 3 meat pies in total. So that leaves two meat pies left. 
So basically, we divide the meat pies by the number of friends.
2/6 is 1/3
So each friend needs to eat 1/3 of a meat pie
8 0
4 years ago
DAVID PLZ HELP LAST ONE
Leto [7]

Answer:

1.D

2.c

Step-by-step explanation:

f(m/4)=8(m²/16)-4(m/4)

=m²/2-m

f(-4)=-3(-4)²+5(-4)

=-3(16)-20

=-48-20

=-68

3 0
3 years ago
Read 2 more answers
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