Question

In right triangle ABC, angle c is a right angle and sin A= sin B. What is m

Answer 1

which

In plane trigonometry, the sine theorem or also known as the law of sines is a ratio between the lengths of the sides of a triangle and the sines of their corresponding opposite angles.

it is

`(a)/(\sin A)=(b)/(\sin B)`

According to the question Sin A=Sin B, so

`a=b`

wich means that this right traingle has two equal sides

if the two sides of a right triangle have the same length, then, they form the same angle with the hypotenuse

also, the question says that C=90 °

we know the sum of the internal angles on a triangle must be 180 °,then

`\begin{gathered} A+B+C=180 \\ A=B \\ 2A+C=180 \\ A=(180-C)/(2) \\ A=(90)/(2) \\ A=45\text{ \degree} \\ B=45\text{\degree} \end{gathered}`

so the answer is B)45 °