What is the value of sin∠ACD?

Question

asked Sep 8, 2023 69.2k views

2 Answers

Tom Bascom · Answer 1 · 2023-09-13T10:25:28+0000

Answer:

Answer is 4/5

Explanation:

» From trigonometric ratios of sine:

${ \tt{ \red{ \sin( \theta) = (opposite)/(hypotenuse) }}} \\$

» But from the triangle given;

• Opposite:

${ \tt{opposite = (12 + 12) \: ft}} \\ { \underline{ \tt{ \: opposite = 24 \: ft \: }}}$

• Hypotenuse:

${ \tt{hypotenuse = (15 + 15) \: ft}} \\ { \underline{ \tt{ \: hypotenuse = 30 \: ft \: }}}$

» Therefore, let's find the sine of angle ACD;

${ \tt{ \sin( \angle ACD) = (24)/(30) }} \\ \\ { \boxed{ \blue{ \tt{ \: \sin( \angle ACD) = (4)/(5) \: }}}}$