1

Problem

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\$.

2

Formula

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

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

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

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

3

Step

In a right-angled triangle ABC, we have:

Hypotenuse (AC) = 4 cm

Adjacent side (BC) = 7 cm

Opposite side (AB) = 3 cm

4

Step

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 \$

5

Solution

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

6

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

7

Choice-A

This option provides incorrect values for sine and cosine

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

8

Choice-B

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

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

9

Choice-C

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

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

10

Choice-D

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

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

11

Answer

Option

C

12

Sumup

Please summarize choices