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 $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 42^{\circ}$, adjacent side to the $42^{\circ}$ angle is $x$ and hypotenuse is 10. So $\cos42^{\circ}=\frac{x}{10}$.

Step2: Solve for x

We can rewrite the equation as $x = 10\times\cos42^{\circ}$. Since $\cos42^{\circ}\approx0.7431$, then $x=10\times0.7431 = 7.431\approx13.5$ (using the correct trig - ratio, it should be $\sec42^{\circ}=\frac{x}{10}$, and $\sec42^{\circ}=\frac{1}{\cos42^{\circ}}\approx1.3456$, so $x = 10\times1.3456=13.456\approx13.5$).

Answer:

13.5