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3 years ago

15

the volume of a solid triangular prism is 726 cubic centimeters. its height is 12 centimeters and its bases are congruent right

isosceles triangles. find the lengths of the equal sides of each base.

1 answer:

aivan3 [116]3 years ago

4 0

9514 1404 393

Answer:

11 cm

Step-by-step explanation:

The volume of the prism is given by the formula ...

V = Bh

where B is the area of the triangular base, and h is the height.

Filling in the given information, we find the area of the triangular base to be ...

726 cm³ = B(12 cm)

B = 726 cm³/(12 cm) = 60.5 cm²

The area of an isosceles right triangle is half the area of a square with the same side lengths:

B = 1/2s²

60.5 = 1/2s²

s = √(2(60.5)) = √121 = 11

The length of each of the equal sides of the base is 11 cm.

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Need help on these trig homework

allochka39001 [22]

8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

<h3>How to solve the trigonometry</h3>

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 20 = \frac{x}{23}$

Cross multiply

$sin 20$ × $23 = x$

$x = 0. 3420$ × $23$

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 37. 3 = \frac{x}{19}$

cross multiply

$x = 0. 6059$ × $19$

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$

For side a, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$85^2 = a^2 + 67^2$

$a = \sqrt{89^2-67^2}$

$a = \sqrt{3432}$

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

$\frac{59}{sin A } = \frac{85}{sin 90}$

cross multiply

$sin A$ × $85$ = $sin 90$ × $59$

make sin A subject of formula

$sin A = \frac{59}{85}$

$sin A = 0. 6941$

A = $sin^-^1(0. 6941)$

A = 44°

$\frac{67}{sin B} = \frac{85}{sin 90}$

cross multiply

$sin B$ × $85$ = $sin 90$ × $67$

make sin b subject of formula

$sin B = \frac{67}{85}$

$sin B = 0. 7882$

B = $sin^-^1( 0. 7882)$

B = 52°

4. To find the sides, we use the sine rule;

$\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}$

Cross multiply

$sin 56. 6$ × $c = sin 90$ × $74$

make 'c' subject of formula

$c = \frac{74}{0. 8348}$

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$b^2 = c^2 - a^2$

$b^2 = 88. 8^2 - 74^2$

$b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}$

b = 49. 1 m

$\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}$

cross multiply

$sin B = \frac{40. 99}{74. 0}$

B = $sin^-^1(0. 5539)$

B = 34°

Learn more about trigonometric identity here:

brainly.com/question/7331447

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1 year ago

Use algebra tiles to find the difference. Let one yellow tile equal +1 and one red tile equal –1. 12 – (–11)

Anvisha [2.4K]

Answer:

its 23

Step-by-step explanation:

its 12+11 because two negatives make a positive

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2 years ago

Consider the function f(x)= x² - 4

Arisa [49]

Answer:

(X+2) (X-2) . This is the final answer

Step-by-step explanation:

Solving f(x) = x^2 - 4

A^2 - B^2 is a special case where the original equation before it was foiled is

(A + B) (A - B) because the middle terms will cancel out when foiled.

This means that the equation can be written as

(X + 2)(X - 2) = 0

Each of these you will then set equal to 0 and then solve

X + 2 = 0, X - 2 = 0

X = -2, 2

I hope this helps you! let me now if its right ok <3 :)

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3 years ago

Select from the drop-down menus to correctly complete the statement.

Dominik [7]

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3 years ago

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What is the value of x?<br><br> x-2/5=7

arsen [322]

X=37/5
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