How to solve for a trigonometric equation

I want to solve for x from the following equation;

0.7978 + 0.7978*tan^2(x) = (Hperson * (1 - 0.1591*tan^2(x)))/ Fdist

The Hperson and Fdist are known values or variables. For example if Hperson = 175, Fdist = 120. The x value returned should be approx 38.7 degrees.

Apologies if such a question has been answered before. But I couldnt find a solution. Thank you.

Answer 1

[Star Strider]

Rearrange the equation, then use fzero:

Hperson =  175;
Fdist = 120;
F = @(x) 0.7978 + 0.7978*tand(x).^2 - (Hperson * (1 - 0.1591*tand(x).^2)) / Fdist;  % Create Implicit Expression
x_deg = fzero(F, 45)                                                                % Use ‘fzero’

x_deg =
        38.69

[Sweptix]

I dont understand the use of fzero here. why do we need it? Why cant we just use the F value?

Also following your code sample above, I tried executing the following formula:

Tan(21.75 - x_deg) = (Hperson - Hcamera)/Fdist

as

function [ Tilt, Hcamera] = FindTilt( Hperson, Fdist )
% The function returns the camera tilt and camera height 
% given the Height of the person and working distance
F = @(x) 0.7978 + 0.7978*tand(x).^2 - (Hperson * (1 - 0.1591*tand(x).^2)) / Fdist;  % Create Implicit Expression
x_deg = fzero(F, 45);                                                                % Use ‘fzero’
Tilt = x_deg; 
G = @(Hcamera) tand(21.75 - x_deg) - (175 - Hcamera)/Fdist;
Hcamera
end

For the value of G, Undefined function or variable "Hcamera".

[Star Strider]

The fzero function solves the implicit version of your equation for ‘x’. ‘F’ and ‘G’ in your code are anonymous functions that fzero finds the root of that are nearest the initial estimate (if a real root exists in that region).

You have not provided a definition for ‘Hcamera’ in your function, and you have not passed it to your function as a parameter. Since you apparently want to solve for ‘Hcamera’, use fzero again, with an appropriate initial value:

Hc0 = 100;
Hcamera = fzero(G, Hc0);

and using your previous data for ‘Hperson’ and ‘Fdist’:

Hcamera =
       211.55