Question

find the area of the given triangle. round your answer to the nearest tenth. do not round any intermediate computations. try again your answer is incorrect. square units

Explanation:

Step1: Identify triangle type

It's a right triangle with one leg \( a = 19 \), angle \( \theta = 41^\circ \). Let the other leg be \( b \). Using \( \tan\theta=\frac{b}{a} \), so \( b = a\tan\theta \).
\( b = 19\times\tan(41^\circ) \)

Step2: Calculate area

Area of right triangle: \( A=\frac{1}{2}ab \). Substitute \( a = 19 \), \( b = 19\tan(41^\circ) \).
\( A=\frac{1}{2}\times19\times(19\tan(41^\circ))=\frac{19^2}{2}\tan(41^\circ) \)
\( \tan(41^\circ)\approx0.8693 \), \( 19^2 = 361 \), so \( A=\frac{361}{2}\times0.8693\approx180.5\times0.8693\approx156.9 \)

Answer:

156.9