Answer:
160.70 ft. ( approx )
Step-by-step explanation:
Let AB represents the cliff, C represents Scott's position,
Then according to the question,
m∠ABC = 93°, ( because beach slopes gently at an angle of 3 feet from the horizontal )
m∠ACB = 70°,
BC = 50 ft,
∵ The sum of all interior angles of a triangle is 180°,
i.e. m∠ABC + m∠ACB + m∠BAC = 180°,
⇒ 93° + 70° + m∠BAC = 180°,
⇒ m∠BAC = 180° - 163° = 17°,
By the law of sine,
[tex]\frac{\sin A}{BC}=\frac{\sin C}{AB}[/tex]
[tex]\frac{\sin 17^{\circ}}{50}=\frac{\sin 70^{\circ}}{AB}[/tex]
[tex]\implies AB = \frac{50 sin 70^{\circ}}{sin 17^{\circ}}\approx 160.70[/tex]
Hence, daredevil cliff is approximately 160.70 ft.
