The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width.

1 answer:

4 0

Perimeter is 2l + 2w (l=length w=width) so if l=3+2w and you plug that in you get 2(3+2w)+2w=perimeter.
Distribute to simplify equation
P=6+4w+2w
Then simplify like terms
P=6+6w
Then plug perimeter in
128=6+6w
Solve
122=6w

W=20.333

And plug that in the original equation for length
128=2l+2(20.333)
128=2l+40.666
2l=87.3333

L=43.666

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You hike 190 meters up a steep hill that has a 33∘ angle of elevation as shown in the diagram.

erik [133]

Answer:

b = 159 m

a = 103 m

angle B is 57 degrees

Step-by-step explanation:

Let’s start with getting the measure of angle B

Mathematically, since we have a right triangle , we have to subtract the given angle from 90 to get the other acute angle

So we have the measure of B as;

90-33 = 57 degrees

To get the value of a, we use the appropriate trigonometric ratio

a faces the angle 33, that makes it an opposite to that angle

190 faces the right angle and that makes it the hypotenuse

Mathematically , the relationship between the two is that trigonometrically, they are related by the sine which is the ratio of the opposite to the hypotenuse

so, we have it that;

sine 33 = a/190

a = 190 * sine 33

a = 103 m

to get b, it is adjacent to the given angle

So with the hypotenuse, the ratio between it and the hypotenuse is the cosine

so;

cos 33 = b/190

b = 190 * cos 33

b = 159 m

4 0

3 years ago