Answer:
Ques 11: 123.08 meters.
Ques 12: 269.4 meters.
Ques 13: 211.27 meters.
Step-by-step explanation:
Ques 11: We have that the angle of elevation from the ship to the top of the lighthouse is 18° and the height of the lighthouse is 40 m.
It is required to find the distance of the ship from the shore, say 'x' m.
As, we have, [tex]\tan \theta=\frac{opposite}{adjacent}[/tex]
⇒ [tex]\tan 18=\frac{40}{x}[/tex]
⇒ [tex]x=\frac{40}{\tan 18}[/tex]
⇒ [tex]x=\frac{40}{0.325}[/tex]
⇒ x = 123.08 m.
Thus, the distance of the ship from the shore is 123.08 meters.
Ques 12: We have, length of the kite is 300 m and the angle made by the string is 64°.
It is required to find the height of the kite, say 'x' m.
As, we have, [tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]
⇒ [tex]\sin 64=\frac{x}{300}[/tex]
⇒ [tex]x=300\times \sin 64[/tex]
⇒ [tex]x=300\times 0.898[/tex]
⇒ x = 269.4 m.
Hence, the height of the kite is 269.4 meters.
Ques 13: We have, the wreckage is found at the angle of 12° and the diver is lowered down by 45 meters.
It is required to find the distance covered by the diver to reach the wreckage, say 'x' m.
As, we have, [tex]\tan \theta=\frac{opposite}{adjacent}[/tex]
⇒ [tex]\tan 12=\frac{45}{x}[/tex]
⇒ [tex]x=\frac{45}{\tan 12}[/tex]
⇒ [tex]x=\frac{45}{0.213}[/tex]
⇒ x = 211.27 m.
Thus, the distance covered by the diver to reach the wreckage is 211.27 meters.
