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2 years ago

A skateboarding ramp is 12 in. high and rises at an angle of 21°. How long is the base of the ramp? Round to the nearest inch.

Mathematics

1 answer:

bagirrra123 [75]2 years ago

3 0

Answer:

the base of the ramp is 31 inches long.

Step-by-step explanation:

c = a/sin(α)

= 33.48514

b = √c2 - a2

= √33.4851373155042 - 122

= √977.25442103816

= 31.26107

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In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

erica [24]

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Answer:

$BD = c*sin(A)$

$BD = c*cos(B)$

$BD = b*tan(A)$

Step-by-step explanation:

∆ABD is a right triangle.

Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.

SOH => sin(θ) = opposite/hypotenuse

CAH => Cos(θ) = adjacent/hypotenuse

TOA = tan(θ) = opposite/adjacent

Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:

Let BD = x

AB = c

AD = b

=>The sine ratio for the length of line segment BD = x, using SOH.

θ = A

Opposite = DB = x

hypotenuse = AB = c

$sin(A) = \frac{x}{c}$

Make x the subject of formula.

$c*sin(A) = x$

$BD = x = c*sin(A)$

=>The Cosine ratio for the length of line segment BD = x, using CAH

θ = B

Adjacent = DB = x

hypotenuse = AB = c

$cos(B) = \frac{x}{c}$

Make x the subject of formula.

$c*cos(B) = x$

$BD = x = c*cos(B)$

=>The Tangent ratio for the length of line segment BD = x, using TOA

θ = A

Adjacent = DB = x

hypotenuse = AD = b

$tan(A) = \frac{x}{b}$

Make x the subject of formula.

$b*tan(A) = x$

$BD = x = b*tan(A)$

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3 years ago

La razon de 3 librasa $ 6.00

andrew-mc [135]

Answer:

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2 years ago

Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:(a) the maximum

andreyandreev [35.5K]

Answer and explanation:

Given : Suppose that a die is rolled twice.

The sample space form is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

To find : What are the possible values that the following random variables can take on

(a) The maximum value to appear in the two rolls;

The possible values are 1; 2; 3; 4; 5; 6.

b) The minimum value to appear in the two rolls;

The possible values are 1; 2; 3; 4; 5; 6.

c) The sum of the two rolls;

The possible values are 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12.

d) The value of the first roll minus the value of the second roll.

The possible values are -5; -4; -3; -2; -1; 0; 1; 2; 3; 4; 5.

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3 years ago

How to solve 2x^2 - 4x = 3

zhenek [66]

Answer:

1 ± i(1/2)√2

Step-by-step explanation:

Write this quadratic in standard form: subtract 3 from both sides. This results in 2x^2 - 4x - 3 = 0. Let's apply the quadratic formula. The coefficients of the x terms are 2, -4 and -3, so the discriminant is (-4)^2 - 4(2)(-3), or 16 - 24 = -8.

Following the format of the quadratic formula, we get

-(-4) ±i2√8 4 ±i2√2

x = ----------------- = --------------- = 1 ± i(1/2)√2

4 4

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3 years ago

Mr. Clarke built a deck around the swimming pool and sandbox in his backyard. What is the area of the decking that surrounds the

ss7ja [257]

Answer:

$1,174.8\ ft^{2}$

Step-by-step explanation:

we know that

The area of the decking is equal to the area of the parallelogram minus the area of the pool minus the area of the sand box

Remember that

$21\frac{1}{2}\ ft=21.5\ ft$

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3 years ago

A skateboarding ramp is 12 in. high and rises at an angle of 21​°. How long is the base of the​ ramp? Round to the nearest inch.

A skateboarding ramp is 12 in. high and rises at an angle of 21°. How long is the base of the ramp? Round to the nearest inch.