Ask question

Ask question

All categories

3 years ago

12

A right triangle has base b = 100 plusminus 1 ft and adjacent angle theta = 30 degree plusminus 0.5 degree. Calculate the height

h and its uncertainty.

1 answer:

aivan3 [116]3 years ago

4 0

Answer:

The height h of this right triangle is 57.74±1.74ft.

Explanation:

Knowing that this is a right triangle, if one of the angles adjacent to the base, θ is 30º, the other angle is 90º. Therefore we can calculate the height h can be calculated with the tangent:

$tan(\theta)=\frac{h}{b}\leftrightarrow h=tan(\theta)b=tan(30^\circ)100ft=57.74ft$

For the uncertainty we use the partial derivatives:

$\Delta h=|\frac{dh}{db}|\Delta b+ |\frac{dh}{d\theta}|\Delta \theta\\\Delta h=|tan(\theta)|\Delta b+ |\frac{b}{cos^2(\theta)}|\Delta \theta$

We have to be careful to use Δθ in radians:

$\Delta h=|tan(30^\circ)|1ft+ |\frac{100ft}{cos^2(30^\circ)}|\frac{0.5^\circ2\pi}{360^\circ}=1.74ft$

You might be interested in

Three forces act on a moving object. One force has a magnitude of 83.7 N and is directed due north. Another has a magnitude of 5

LekaFEV [45]

Answer:

$|\vec{F}_3| = 102.92 \ N$

$\theta = 57 \° 24 ' 48''$

Explanation:

For an object to move with constant velocity, the acceleration of the object must be zero:

$\vec{a} = \vec{0}$ .

As the net force equals acceleration multiplied by mass , this must mean:

$\vec{F}_{net} = m \vec{a} = m * \vec{0} = \vec{0}$ .

So, the sum of the three forces must be zero:

$\vec{F}_1 + \vec{F}_2 + \vec{F}_3 = \vec{0}$ ,

this implies:

$\vec{F}_3 = - \vec{F}_1 - \vec{F}_2$ .

To obtain this sum, its easier to work in Cartesian representation.

First we need to define an Frame of reference. Lets put the x axis unit vector $\hat{i}$ pointing east, with the y axis unit vector $\hat{j}$ pointing south, so the positive angle is south of east. For this, we got for the first force:

$\vec{F}_1 = 83.7 \ N \ (-\hat{j})$ ,

as is pointing north, and for the second force:

$\vec{F}_2 = 59.9 \ N \ (-\hat{i})$ ,

as is pointing west.

Now, our third force will be:

$\vec{F}_3 = - 83.7 \ N \ (-\hat{j}) - 59.9 \ N \ (-\hat{i})$

$\vec{F}_3 = 83.7 \ N \ \hat{j} + 59.9 \ N \ \hat{i}$

$\vec{F}_3 = (59.9 \ N , 83.7 \ N )$

But, we need the magnitude and the direction.

To find the magnitude, we can use the Pythagorean theorem.

$|\vec{R}| = \sqrt{R_x^2 + R_y^2}$

$|\vec{F}_3| = \sqrt{(59.9 \ N)^2 + (83.7 \ N)^2}$

$|\vec{F}_3| = 102.92 \ N$

this is the magnitude.

To find the direction, we can use:

$\theta = arctan(\frac{F_{3_y}}{F_{3_x}})$

$\theta = arctan(\frac{83.7 \ N }{ 59.9 \ N })$

$\theta = 57 \° 24 ' 48''$

and this is the angle south of east.

7 0

3 years ago

FREE BRAINLIEST! if you can answer this correctly ill give you brainliest and answer some of the questions you have posted :) th

Gala2k [10]

b) accelerate to the left as much more pressure is pulling it in that direction and on the right however , there is less force .

4 0

3 years ago

Naphthalene combustion can be used to calibrate the heat capacity of a bomb calorimeter. the heat of combustion of naphthalene i

barxatty [35]

My namer js gpvjt ahsdhhsdbdb

6 0

3 years ago

If the mass of the moon is ...

bulgar [2K]

C decreased the factor cuz the max is smaller

8 0

3 years ago

1. A rocket is launched from a 300 cm rail. The upper Launch Lug is placed 1 point 150 cm from the bottom of the rocket. What is

patriot [66]

Answer:

i think its going to be 150 because its half of 300

Explanation:

4 0

2 years ago