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4 years ago

Find the length of the missing side of this right triangle.

Mathematics

1 answer:

NemiM [27]4 years ago

7 0

You want to use the pythagorean theorem here.
a^2 + b^2 = c^2, where a and b are side lengths and c is the hypotenuse.

you're given your hypotenuse -- 6 inches -- and one side -- √3 inches. plug these into your formula:

(√3)^2 + b^2 = 6^2 ... now simplify
3 + b^2 = 36 ... subtract 3
b^2 = 33 ... cancel out the exponent by taking the sq root of both sides
b = √33 inches is your missing length.

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3 years ago

the perimeter of the circular base of a cone is 132 cm and its vertical height is 28 cm find the curved surface area total surfa

Elden [556K]

Answer:

i. Curved surface area = 2310 $cm^{2}$

ii. Total surface area = 3696 $cm^{2}$

iii. volume = 12936 $cm^{3}$

Step-by-step explanation:

Perimeter of the circular base = circumference of the circle = 132 cm

circumference of a circle = 2 $\pi$ r

132 = 2 $\pi$ r

r = $\frac{132}{2\pi }$

= $\frac{66}{\pi }$

r = 66 x $\frac{7}{22}$

= 3 x 7

= 21

radius = 21 cm

vertical height, h = 28 cm

Thus applying the Pythagoras theorem,

$l^{2}$ = $h^{2}$ + $r^{2}$

= $28^{2}$ + $21^{2}$

= 784 + 441

= 1225

l = $\sqrt{1225}$

l = 35 cm

The slant height is 35 cm.

i. Curved surface area = $\pi$ rl

= $\frac{22}{7}$ x 21 x 35

= 22 x 3 x 35

= 2310

curved surface area of the cone is 2310 $cm^{2}$ .

ii. Total surface area = $\pi r^{2}$ + $\pi$ rl

= $\pi$ r(r + l)

= $\frac{22}{7}$ x 21 (21 + 35)

= 22 x 3 x 56

= 3696

The total surface area of the cone is 3696 $cm^{2}$ .

iii. volume of a cone = $\frac{1}{3}$ $\pi r^{2}$ h

= $\frac{1}{3}$ x $\frac{22}{7}$ x $21^{2}$ x 28

= 12936

The volume of the cone is 12936 $cm^{3}$

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3 years ago

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,

Mandarinka [93]

Answer:

C is the equation that is perpendicular and goes through the given point.

Step-by-step explanation:

In order to find this, we first need to find an equation with the appropriate slope. Perpendicular lines have opposite and reciprocal slopes. Since the slope of the original line is 1, we need a line with -1 slope. C and D are the only such answers that have this slope.

Next we look for it to fit into the following point slope equation.

y - y1 =m(x - x1)

We use the point (2, 5) as (x1, y1). So we can plug those in the spots that we see above as well as the slope at m.

y - y1 =m(x - x1)

y - 5 = -(x - 2)

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4 years ago