# how to solve equation to find angle

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I have the values of variables be like:

clear;

Vau = 43.0;

Vsu = 47.45;

beta = 1.41;

gamma = 5/3;

syms theta_u

I wish to find the value of theta_u.

For this, I have an equation like

when i solved this equation it turns out to be like

Now I put this equation for solving it to matlab using code:

Q3 = double(solve(Vsu*(cosd(theta_u*(sqrt(2/(beta*gamma)))))*(1/(Vau*(cosd(theta_u))))-1))

it gives an error

Q3 = double(solve(Vsu*(cosd(theta_u*(sqrt(2/(beta*gamma)))))*(1/(Vau*(cosd(theta_u))))-1))

Warning: Unable to solve symbolically. Returning a numeric approximation instead.

> In solve (line 304)

Q3 =

-162.2052

which is also a wrong answer. The correct answer is 71.8. Please suggest if there are any corrections.

##### 2 Comments

Alan Stevens
on 29 Aug 2020

VBBV
on 8 Sep 2020

Place the term in sqrt outside the cost parenthesis

Try this

Q3 = solve(sqrt((beta*gamma)/2)*acos((sin(theta_u)*Vau)/Vsu),theta_u)

You will get two values ...

Q3 =

asin(949/860)

pi - asin(949/860)

Multply the first real(asin(949/860)*180/pi)

To get 90 deg

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