$tan\theta=\frac{sin\theta}{cos\theta}\\\\\\Look\ at\ the\ picture.\\\\In\ a\ right\ triangle:\\\\sin\theta=\frac{a}{c};\ cos\theta=\frac{b}{c};\ tan\theta=\frac{a}{b}\\\\\frac{sin\theta}{cos\theta}=\frac{\frac{a}{c}}{\frac{b}{c}}=\frac{a}{c}\times\frac{c}{b}=\frac{a}{b}=tan\theta$

3 0

3 years ago

Conrad had $110 to spend on 9 cheese pizzas for a party. After buying them, he had $8.75 left. How much did each pizza cost? Sho

Igoryamba

Subtract 110 and 8.75 and you get 101.25 then divide that by 9 and you get 11.25

3 0

3 years ago

Find the island height of a pyramid with a volume of 432 ft^3 if the base is a square with a side length of 12 ft. Round to the

dmitriy555 [2]

So the picture below shows what the slant height is. It also shows that the pyramid can form a right triangle, in which we can use the pythagorean theorem, which is $leg^2+leg^2=hypotenuse^2$ .

But first, we have to find the height of this pyramid. The volume formula for a square pyramid is $A=\frac{lwh}{3}$ . Since we know its a square pyramid, the length and width are going to be the same (12 ft), and we know that the volume is 432 ft^3. Using this info, we can solve for the height:

$432=\frac{12*12*h}{3}\\ 1296=12*12*h\\ 1296=144*h\\ 9=h$

So now we can use the pythagorean theorem (remember to split the 12 by 2, since the right triangle has only half the length of the base). Our equation will be solved as such:

$6^2+9^2=s^2\\ 36+81=s^2\\ 117=s^2\\ 10.8=s$

In short, the slant height is 10.8 ft.

3 0

3 years ago

Colton is filling 5 aquariums with water. Each aquarium needs 72 gallons of water. About how many gallons of water are needed to

Natali5045456 [20]

A. about 14
divide 72/5= 14.4 which rounds to 14

4 0

3 years ago

3(8 - 2x) + 2(7x -19)simplify​

3(8 - 2x) + 2(7x -19)simplify