Mathematics: How can I find unknown angle t ?

Mathematics : asked on sahrsalim70

17.07.2022

How can I find unknown angle t ?

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24.01.2023, solved by verified expert

Nitin Arora

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Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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Answer:

t = 12.64 ft.

Step-by-step explanation:

How can I find unknown angle t ?, №15256447, 17.07.2022 21:37

From the given figure, CE = CB - EB = CB - DA = 15 - 3 = 12 ft

Now, in triangle DCE,

DC = t ft.

CE = 12 ft.

DE = 4 ft.

using pythagoras theorem,

DC^2 = CE^2 + DE^2

t^2 = 12^2 + 4^2 = 144 + 16 = 160

t = sqrt(160) = 12.64 ft.

Hence, t = 12.64 ft.

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Mathematics

Solving for Unknown Angles Lines x and y are parallel. Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank. Use the diagram to determine the measure of the unknown angle. m∠1 = (6x + 8)° m∠1 = 74° What is the value of x? What is the measure

Step-by-step answer

P Answered by Specialist

x=11

Step-by-step explanation:

x=11 because, 6x+8= 74, so you do 74-8=66 and 66/6= 11. so x=11,

the measure of 2 is 7(11)-2+m=106.

so you add 2 on both sides to cancel it out, and you end up with 7(11)+m=108

now you do 7(11)= 77, and you subtract from both sides and get 31.

therefore, m=31.

hope this helps!

Mathematics

Lorie correctly determines that for the triangles below, the statement Triangle N M O is similar to triangle T S R and the statement Triangle N M O is similar to triangle T R S both describe the relationship between the two triangles. Triangle M N O. Angle M is 54.4 degrees and angle N is 71.2 degrees. Triangle R S T. Angle R is 54.4 degrees and angle T is 71.2 degrees. Which best describes why both similarity statements are correct? Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S. Each

Step-by-step answer

P Answered by PhD

(A)Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S.

Step-by-step explanation:

In Triangle MNO

$\angle M = 54.4$ degrees, \angle N = 71.2$ degrees\\\angle M+\angle N+\angle O=180^\circ\\54.4^\circ+71.2^\circ+\angle O=180^\circ\\\angle O=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ$

In Triangle RST

$\angle R = 54.4$ degrees, \angle T = 71.2$ degrees\\\angle R+\angle T+\angle S=180^\circ\\54.4^\circ+71.2^\circ+\angle S=180^\circ\\\angle S=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ$

Therefore:

Triangle NMO is congruent to triangle TSR; and

Triangle NMO is congruent to triangle TRS

This is because

$\angle M \cong \angle O =54.4^\circ; and\\ \angle R \cong \angle S =54.4^\circ .$

The correct option is A.

Mathematics

Step-by-step answer

P Answered by Specialist

x=11

Step-by-step explanation:

x=11 because, 6x+8= 74, so you do 74-8=66 and 66/6= 11. so x=11,

the measure of 2 is 7(11)-2+m=106.

so you add 2 on both sides to cancel it out, and you end up with 7(11)+m=108

now you do 7(11)= 77, and you subtract from both sides and get 31.

therefore, m=31.

hope this helps!

Physics

1. a man stands on top of a 25 m tall cliff. the man throws a rock upwards at a 25-degree angle above the horizontal with an initial velocity of 7.2 m/s. what will be the vertical position of the rock at t = 2 seconds? what will be the horizontal position of the rock at that time? 2. a cannon fires a cannonball forward at a velocity of 48.1 m/s horizontally. if the cannon is on a mounted wagon 1.5 m tall, how far would the cannonball travel before it lands on the ground? 3. look at the following picture. what would be the resultant vector of a+b?

Step-by-step answer

P Answered by PhD

y = 11.48 m

x = 13.0 m

Explanation:

Components of initial velocity is given as

v_x = 7.2 cos25 = 6.52 m/s

v_y = 7.2 sin25 = 3.04 m/s

Now after t = 2 s the vertical position is given as

$y = y_0 + v_y t + \frac{1}{2}a_y t^2$

$y = 25 + 3.04(2) - \frac{1}{2}(9.8)(2^2)$

y = 11.48 m

Now horizontal position is given as

x = v_x t

$x = 6.52 \times 2$

x = 13.04 m

d = 26.6 m

Explanation:

Initial position on y axis is given as

y = 1.5 m

velocity of ball in y direction

v_y = 0

now we have

$\Delta y = v_y t + \frac{1}{2}gt^2$

$1.5 = \frac{1}{2}(9.8) t^2$

t = 0.55 s

now the distance moved by the ball in horizontal direction is given as

d = v_x t

$d = 48.1 \times 0.55$

d = 26.6 m

$A + B = 12.42\hat i + 0.35 \hat j$

Explanation:

Here we can see the two vectors inclined at different angles

so two components of vector A is given as

$A = 11.3 cos21\hat i - 11.3 sin21\hat j$

$A = 10.55 \hat i - 4.05 \hat j$

Similarly for other vector B we have

$B = 4.78cos67 \hat i + 4.78 sin67\hat j$

$B = 1.87\hat i + 4.4 \hat j$

now we need to find A + B

so we have

$A + B = (10.55\hat i - 4.05\hat j) + (1.87\hat i + 4.4 \hat j)$

$A + B = 12.42\hat i + 0.35 \hat j$

d = 81.86 m

Explanation:

Displacement of airplane is given as

d_1 = 72 km in direction 30 degree East of North

$d_1 = 72sin30\hat i + 72cos30\hat j$

$d_1 = 36\hat i + 62.35\hat j$

d_2 = 48 km South

$d_2 = -48\hat j$

d_3 = 100 km in direction 30 degree North of West

$d_3 = -100 cos30\hat i + 100 sin30\hat j$

$d_3 = -86.6\hat i + 50\hat j$

so net displacement is given as

d = d_1 + d_2 + d_3

$d = 36\hat i + 62.35\hat j - 48\hat j - 86.6\hat i + 50 \hat j$

$d = -50.6\hat i + 64.35\hat j$

now magnitude of displacement is given as

$d = \sqrt{50.6^2 + 64.35^2}$

d = 81.86 m

1) final speed at which it will hit the ground again

2) acceleration during the motion of the ball

Explanation:

As we know that the speed at which the ball is thrown is always same to the speed by which it will hit back on the ground

so we know that final speed will be same as initial speed

Also we know that during the motion the acceleration of ball is due to gravity so it will be

a = - g

Physics

Step-by-step answer

P Answered by PhD

y = 11.48 m

x = 13.0 m

Explanation:

Components of initial velocity is given as

v_x = 7.2 cos25 = 6.52 m/s

v_y = 7.2 sin25 = 3.04 m/s

Now after t = 2 s the vertical position is given as

$y = y_0 + v_y t + \frac{1}{2}a_y t^2$

$y = 25 + 3.04(2) - \frac{1}{2}(9.8)(2^2)$

y = 11.48 m

Now horizontal position is given as

x = v_x t

$x = 6.52 \times 2$

x = 13.04 m

d = 26.6 m

Explanation:

Initial position on y axis is given as

y = 1.5 m

velocity of ball in y direction

v_y = 0

now we have

$\Delta y = v_y t + \frac{1}{2}gt^2$

$1.5 = \frac{1}{2}(9.8) t^2$

t = 0.55 s

now the distance moved by the ball in horizontal direction is given as

d = v_x t

$d = 48.1 \times 0.55$

d = 26.6 m

$A + B = 12.42\hat i + 0.35 \hat j$

Explanation:

Here we can see the two vectors inclined at different angles

so two components of vector A is given as

$A = 11.3 cos21\hat i - 11.3 sin21\hat j$

$A = 10.55 \hat i - 4.05 \hat j$

Similarly for other vector B we have

$B = 4.78cos67 \hat i + 4.78 sin67\hat j$

$B = 1.87\hat i + 4.4 \hat j$

now we need to find A + B

so we have

$A + B = (10.55\hat i - 4.05\hat j) + (1.87\hat i + 4.4 \hat j)$

$A + B = 12.42\hat i + 0.35 \hat j$

d = 81.86 m

Explanation:

Displacement of airplane is given as

d_1 = 72 km in direction 30 degree East of North

$d_1 = 72sin30\hat i + 72cos30\hat j$

$d_1 = 36\hat i + 62.35\hat j$

d_2 = 48 km South

$d_2 = -48\hat j$

d_3 = 100 km in direction 30 degree North of West

$d_3 = -100 cos30\hat i + 100 sin30\hat j$

$d_3 = -86.6\hat i + 50\hat j$

so net displacement is given as

d = d_1 + d_2 + d_3

$d = 36\hat i + 62.35\hat j - 48\hat j - 86.6\hat i + 50 \hat j$

$d = -50.6\hat i + 64.35\hat j$

now magnitude of displacement is given as

$d = \sqrt{50.6^2 + 64.35^2}$

d = 81.86 m

1) final speed at which it will hit the ground again

2) acceleration during the motion of the ball

Explanation:

As we know that the speed at which the ball is thrown is always same to the speed by which it will hit back on the ground

so we know that final speed will be same as initial speed

Also we know that during the motion the acceleration of ball is due to gravity so it will be

a = - g

Mathematics

Can you guys help me please Find the measures of the unknown angle Don’t answer if you do not know .

Step-by-step answer

P Answered by Master

Below

Step-by-step explanation:

Angle A= 65 degrees

Angle N= 53 degrees

Angle L= 45

4th image= x=30

2x=60

5th image= x=50

x+30=80

Please tell me if this helps!

Mathematics

25 points! choose all that correctly computes the unknown angle.∠w = 31°∠x = 149°∠y = 31°∠z = 90° you, i don t have a lot of time left, but some would be appreciated!

Step-by-step answer

P Answered by Specialist

We have z = 90•
x = 59 + z
w = y = 180 - x
So x = 59 + 90 = 149•
w = y = 180 - 149 = 31•
All answers are correct.

Mathematics

Can you guys help me please Find the measures of the unknown angle Don’t answer if you do not know .

Step-by-step answer

P Answered by Specialist

Below

Step-by-step explanation:

Angle A= 65 degrees

Angle N= 53 degrees

Angle L= 45

4th image= x=30

2x=60

5th image= x=50

x+30=80

Please tell me if this helps!

Mathematics

25 points! choose all that correctly computes the unknown angle.∠w = 31°∠x = 149°∠y = 31°∠z = 90° you, i don t have a lot of time left, but some would be appreciated!

Step-by-step answer

P Answered by Specialist

We have z = 90•
x = 59 + z
w = y = 180 - x
So x = 59 + 90 = 149•
w = y = 180 - 149 = 31•
All answers are correct.

Mathematics

The angle measures of quadrilateral rstu are shown. m∠r = (2x)° m∠s = (3x – 35)° m∠t = (x + 35)° the measure of angle u is unknown. can quadrilateral rstu be a parallelogram? a. yes, opposite angles r and t can be made equal to each other if x = 35. b. yes, consecutive angles r and s can be made equal to each other if x = 35. c. no, if x = 35, all three given angles measure 70°. the fourth angle would measure 150°. d. no, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral. the correct answer is c.

Step-by-step answer

P Answered by PhD

If <R=<T
2x=x+35
x=35
<R=<T=2*35=70

<S=3x-35=3*35-35=2*35=70

but <R+<S+<T+<U=360
<U=360- (70+70+70)
<U=360-210
<U=150
Impossible to be a parallelogram
C is the answer

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