If in a right-angled triangle ABC, right-angled at B, hypotenuse AC = 4cm, base BC = 7cm, and perpendicular AB = 3cm and if ∠ACB = \$ \theta\$, then find tan \$ \theta\$, sin \$ \theta\$, and cos \$ \theta\$.

In a right-angled triangle ABC, use the following trigonometric ratios:

\$"tan"(\theta) = ("Opposite")/("Adjacent") \$

\$"sin"(\theta) = ("Opposite")/("Hypotenuse")\$

\$"cos"(\theta) = ("Adjacent")/("Hypotenuse")\$

In a right-angled triangle ABC, we have:

Hypotenuse (AC) = 4 cm

Adjacent side (BC) = 7 cm

Opposite side (AB) = 3 cm

Now let’s calculate the trigonometric ratios:

\$ "tan"(\theta) = ("AB")/("BC") = 3/7\$

\$"sin"(\theta) = ("AB")/("AC") = 3/4\$

\$"cos"(\theta) = ("BC")/("AC") = 7/4 \$

So, the values are \$"tan" \theta = 3/7\$, \$"sin" \theta = 3/4\$, \$"cos" \theta = 7/4\$.

This option provides incorrect values for sine and cosine

\$tan \theta = 3/7, sin \theta = 4/3, cos \theta = 7/4\$

This option provides the correct tangent and sine values but an incorrect cosine value

\$tan \theta = 3/7, sin \theta = 3/4, cos \theta = 4/7\$

This choice provides the correct values for tangent, sine, and cosine in the given right-angled triangle scenario

\$tan \theta = 3/7, sin \theta = 3/4, cos \theta = 7/4\$

This option provides incorrect tangent and sine values along with a correct cosine value

\$tan \theta = 7/3, sin \theta = 4/3, cos \theta = 7/4\$

Option

C

Can you summarize what you’ve understood in the above steps?