Question

mustafa is flying a kite, and ana is watching from 20 m away, as shown. from ana’s perspective, the angle between mustafa and his kite is 109°. the length of the string between mustafa and the kite is 46 m. from mustafa’s perspective, what is the angle between ana and the kite? do not round during your calculations. round your final answer to the nearest degree.

Explanation:

Step1: Identify the triangle parts

We have a triangle with sides: \( a = 20 \) m (Mustafa to Ana), \( b = 46 \) m (Mustafa to Kite), angle \( C = 109^\circ \) (Ana's angle), and we need to find angle \( A \) (Mustafa's angle between Ana and Kite). Use the Law of Sines: \( \frac{\sin A}{a}=\frac{\sin C}{b} \)

Step2: Rearrange for \( \sin A \)

\( \sin A=\frac{a\sin C}{b} \)
Substitute \( a = 20 \), \( C = 109^\circ \), \( b = 46 \):
\( \sin A=\frac{20\sin(109^\circ)}{46} \)
Calculate \( \sin(109^\circ)\approx\sin(180 - 71)^\circ=\sin(71^\circ)\approx0.9455 \)
\( \sin A=\frac{20\times0.9455}{46}=\frac{18.91}{46}\approx0.4111 \)

Step3: Find angle \( A \)

\( A=\arcsin(0.4111)\approx24.3^\circ\approx24^\circ \)

Answer:

24