Question

I need to find the missing angle measurement or side length using trig ratios

Answer 1

The given triangle ACB is a right angle triangle with 90 degree at angle C

From the figure we have;

Angle C = 90

CB = 11.9

AC = 10

We need to find the value of angle A and the side AB

For angle Ө;

The side Adjacent to angle Ө is AC and the opposite side to angle Ө is CB

Thus., From the trigonometric ratio;

The ratio of the Opposite side to the adjacent side the tangent of the angle.

`\tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}`

Substitute the value, Opposite side BC = 11.9 and Adjacent side AC = 10

`\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan \theta=(BC)/(AC) \\ \tan \theta=(11.9)/(10) \\ \tan \theta=1.19 \\ \theta=\tan ^(-1)(1.19) \\ \theta=49.95^o \end{gathered}`

Thus, the missing angle is 49.95°

Now, for the side AB;

Apply the trignometric ratio of sin of angle 49.95°

The ratio of the adjacent side to the hypotenuse is the sine of the angle.

`Sin\theta=\frac{Adjacent\text{ Side}}{\text{Hypotenuse}}`

Substitute the value; Adjacent side AC = 10 and Hypotenuse AB and sin 49.95° = 0.765

`Sin\theta=\frac{Adjacent\text{ Side}}{\text{Hypotenuse}}`