Question

In this triangle, which of the following is true?A. The measure of x is 55° and a = 5.74.B. The measure of x is 35º and a = 5.74.WC. The measure of xis 35º and a = 8.19.D. The measure of xis 55° and a = 11.47.

Answer 1

The given figure is a right triangle, and the sum of two acute angles other than the 90 degree is always 90.

So the equation will be :

$x+55=90$

Solve for the value of x :

x = 90 - 55

x = 35

Use sine function in finding the value of a :

Note that :

$\sin \alpha=\frac{\text{ opposite}}{\text{ hypotenuse}}$

Where alpha is the angle equal to 55,

"a" is the opposite side

and

10 is the hypotenuse

$\begin{gathered} \sin 55=\frac{a}{10} \\ a=10\sin 55 \\ a=8.19 \end{gathered}$

Therefore, the correct answer is Option C.