Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information. text should be lower case.
calculate the value for x.
answer (round to 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Identify trigonometric ratio

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In the right - triangle, the angle $\theta = 42^{\circ}$, the adjacent side to the $42^{\circ}$ angle is the side of length 10, and the hypotenuse is $x$. So, $\cos42^{\circ}=\frac{10}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\cos42^{\circ}=\frac{10}{x}$ to $x=\frac{10}{\cos42^{\circ}}$. Since $\cos42^{\circ}\approx0.7431$, then $x=\frac{10}{0.7431}\approx13.5$.

Answer:

13.5