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4 years ago

A right triangle has one angle that measures 59º. What is the measure of the other acute angle?

Mathematics

1 answer:

photoshop1234 [79]4 years ago

8 0

Answer: 31°

Step-by-step explanation:

We know that a right triangle is equal to 180°. Since this is a right triangle, we know that one angle is 90°. Since we are given out other angle, it is very easy to find the missing angle.

180°=59°+90°+x

180°=149°+x

x=31°

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Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is pi/3. What is the length of the

patriot [66]

We are given two sides of a triangle that are 2 and 5 and the angle between them is pi/3 or 60 degrees. In this case, we can use the cosine law to relate the given dimensions and angle. The cosine rule goes c2 = a2 + b2 - 2abcos C; Substituting, c2 = 4 + 25 - 2*2*5*cos pi/3 ; c2 = 19; c = sqrt 19 = 4.36 units.

4 0

4 years ago

Read 2 more answers

Can someone solve then explain the process of solving this?

lorasvet [3.4K]

Answer:

58°

Step-by-step explanation:

<h3>Angle sum property of triangle:</h3>

The sum of all angles of a triangle is 180°.

x + 69 + 55 + x + 78 = 180

x + x + 69 + 55 + 78 = 180

Combine like terms,

2x + 202 = 180

Subtract 202 from both sides,

2x = 180 - 202

2x = -22

Divide both sides by 2,

x = -22/2

x = -11

∠A = x + 69

= -11 + 69

$\sf \boxed{\angle A= 58^\circ}$

7 0

2 years ago

BRAINLY

Ksivusya [100]

The answer would be m>-4

8 0

3 years ago

Solve for the missing side to the nearest tenth.<br> 19<br> X<br> 51

telo118 [61]

Answer:

<em>x = 30.2 units</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

Selecting any of the acute angles, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.

The given right triangle has an angle of measure 51° and its adjacent leg has a measure of 19 units. It's required to calculate the hypotenuse of the triangle.

We use the cosine ratio to calculate x:

$\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 51^\circ=\frac{19}{x}$

Solving for x:

$\displaystyle x=\frac{19}{\cos 51^\circ}$

$\displaystyle x=\frac{19}{0.6293}$

x = 30.2 units

3 0

3 years ago

A differential equation and a nontrivial solution f are given below. Find a second linearly independent solution using reduction

ki77a [65]

Answer:

The second linearly independent solution is

g(t) = = -(4/9)(3t + 1)

Step-by-step explanation:

Given the differential equation

tx'' - (3t + 1)x' + 3x = 0 ...................(1)

and a solution

f(t) = 4e^(3t)

We want to find a second linearly independent solution g(t), using the method of reduction of order.

Let this second solution be

x = uf(t)

x = u. 4e^(3t) ...................................(2)

x' = u'. 4e^(3t) + u. 12e^(3t) ...........(3)

x'' = u''. 4e^(3t) + u'. 12e^(3t) + u'. 12e^(3t) + u. 36e^(3t)

= 4u''e^(3t) + 24u'e^(3t) + 36ue^(3t) .............(4)

Using the values of x, x', and x'' in (2), (3), and (4) in (1), we have

t[4u''e^(3t) + 24u'e^(3t) + 36ue^(3t)] - (3x + 1)[u'. 4e^(3t) + u. 12e^(3t)] + 3u. 4e^(3t) = 0

4tu''e^(3t) + (12t - 4)u'e^(3t) = 0......(5)

Let w = u'

then w' = u''

(5) now becomes

4tw'e^(3t) + (12t - 4)we^(3t) = 0

4tw'e^(3t) = (4 - 12t)we^(3t)

w'/w = (4 - 12t)/4t = (1/t) - 3

Integrating this, assuming all constants of integration are 0, we have

lnw = lnt - 3t

w = e^(lnt - 3t) = e^(lnt)e^(-3t)

w = te^(-3t)

But remember w = u'

=> u' = te^(-3t)

Integrating this, by part, taking constant of integration as 0, we have

u = -(1/9)(3t + 1)e^(-3t)

Using this in (2)

x = 4 [-(1/9)(3t + 1)e^(-3t)]e^(3t)

= -(4/9)(3t + 1)

And this is what we are looking for.

8 0

3 years ago