Consider this right angle

Mathematics

2 answers:

Zarrin [17]3 years ago

8 0

To solve this problem you must apply the proccedure shown below:

1. You have that the ratio of the tangent function is:

tan(angle)=opposite/adjacent

2. Keeping this on mind, you have:

tan(A)=12/5

Therefore, the answer is:

tan(A)=12/5

Sunny_sXe [5.5K]3 years ago

4 0

Hello!

First you have to label the sides of the triangle

The hypotenuse is the longest side
The opposite side is the side opposite of the angle
The adjacent side is the third side

Find tangent you do opposite / adjacent

The opposite side is 12
The adjacent side is 5

Put in the numbers

The answer is D) 12/5

Hope this helps!

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$