Question

Find x and explain how you found it!

Answer 1

Answer:

$\Large\boxed{\sf x = 19.2}$

Step-by-step explanation:

Here a right angled triangle is given to us and we need to find out the value of x . The measure of one of the sides is 24 and one of the acute angle is 53° .

• Here 24 is hypotenuse of the triangle and x is the perpendicular .

So here we may use the ratio of sine as ,

$\sf\qquad\longrightarrow sin\theta =\dfrac{p}{h}$

• On substituting the respective values ,

$\sf\qquad\longrightarrow sin53^\circ =\dfrac{x}{24}$

Substitute the value of sin 53° = 4/5 ,

$\sf\qquad\longrightarrow \dfrac{4}{5}=\dfrac{x}{24}$

Cross multiply ,

$\sf\qquad\longrightarrow x =\dfrac{24*4}{5}$

Simplify,

$\sf\qquad\longrightarrow \frak{\pink{x =19.2}}$

$\rule{200}4$

Answer 2

Here we use trigonometric ratios

$\\ \rm\hookrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}$

$\\ \rm\hookrightarrow sin53=\dfrac{x}{24}$

$\\ \rm\hookrightarrow 0.8(24)=x$

$\\ \rm\hookrightarrow x=19.2$