Question

what is the approximate value of \\(x\\) in the diagram below? (hint: you will need to use one of the trigonometric ratios given in the table.)

\\(\sin 43^\circ \approx 0.682\\)
\\(\cos 43^\circ \approx 0.731\\)
\\(\tan 43^\circ \approx 0.933\\)

a. 19.74
b. 28.94
c. 39.59
d. 25.19
e. 18.41
f. 36.94

Explanation:

Identify the given values and target variable

Using the Trigonometric Ratios knowledge point

$$
LATEXBLOCK0
$$

Select the appropriate trigonometric ratio

Using the Sine Ratio knowledge point

$$ \sin(43^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{27}{x} $$

Solve for the unknown variable x

Using the Sine Ratio knowledge point

$$
LATEXBLOCK1
$$

Match with the given options

Using the Trigonometric Ratios knowledge point

$$ x \approx 39.59 $$

Answer:

• A. 19.74
• B. 28.94
• C. 39.59 (Correct answer)
• D. 25.19
• E. 18.41
• F. 36.94