The measure of b is..

Mathematics

2 answers:

sladkih [1.3K]3 years ago

7 0

Answer:

b =21

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

20^2 + b^2 = 29^1

400 + b^2 =841

Subtract 400 from each side

b^2 = 441

Take the square root of each side

sqrt(b^2) = sqrt(441)

b =21

ra1l [238]3 years ago

7 0

Answer:

b = 21

Step-by-step explanation:

Ok so solving this is actually really simple.

We need to use the Pythageorum Theorum formula which is $a^2+b^2=c^2$ .

So we already know the c and b which are 29 and 20 and we are trying to find b or a in the formula so.

We have to plug the numbers 29 and 20 into the formula and do the steps which is to sqaure them. So 29 and 20 squared are 841 and 400.

So we have to plug those numbers into the formula and it looks like this now $a^2+400=841$ . So now we have to get a squared alone and to do tha we subtract 400 from 841 which is 441. So now to find a we have to find the square root of a and 441 which is a and 21 so b is 21.

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Effectus [21]

Step-by-step explanation:

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7 0

4 years ago

Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re

fiasKO [112]

Answer: $R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}$

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts $38^{\circ}$ angle to each other

The resultant of the two forces is given by

$\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}$

Insert the values

$\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb$

Resultant makes an angle of

$\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}$