Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
cos θ = 0.8192 A = 45 H = ?
Using the table of trigonometric values, we can find the angle θ by looking up the inverse cosine of 0.8192. This value is approximately 35 degrees.
However, in the given problem, the angle A is given as 45 degrees. This means that the angle θ is a complement of angle A in a right triangle, since the sum of the two acute angles in a right triangle is always 90 degrees. Therefore, θ = 90 - 45 = 45 degrees.
To find H, we can use the sine function, since H is the side opposite to angle θ in the right triangle. Since sin θ = opposite / hypotenuse, we have sin 45 = H / A. Rearranging the equation gives H = A*sin 45 = 45*sin 45 = 45*0.7071 = 31.8165 (rounded to four decimal places).
Therefore, H is approximately 32 (rounded to the nearest degree).