Question

A right angle triangle is shown with hypotenuse equal to 13 centimeters. An acute angle of the triangle is labeled as x degrees. The side adjacent to the acute angle has length 5 centimeters and the side opposite to the acute angle has length 12 centimeters.

What is the value of sin x°?

Answer 1

sin = opposite/hypotenuse

so sin (x) = 12/13

answer is 12/13

Answer 2

Answer:

the right answer is 12/13= 0.92

Step-by-step explanation:

with the data given we have:

with the picture, we already have an idea of the data, and the question asks us to find the sin of x, remembering $sin=$ $\frac{opposite}{hypotenuse}$

so we need to find the value of the opposite

Using the Pythagoras theorem $opposite^{2}$+$adjacent^{2}$= $hypotenuse^{2}$

rewriting

$opposite^{2}$=$hypotenuse^{2}$-$adjacent^{2}$

opposite= $\sqrt{hypotenuse^{2}-adjacent^{2}}$

replacing we have

opposyte= $\sqrt({13^{2} }- 5^{2})$

opposyte=$\sqrt{169-25}$

opposyte= $\sqrt{144}$

opposyte= 12

now replaced in the formula of sin we have

$sinx=$$\frac{opposite}{hypotenuse}$  

sinx=12/13

sinx=0.92