Question

Trigonometry . What

Answer 1

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, $\tan \theta=\frac{opposite}{adjacent}$

⇒ $\tan 18=\frac{40}{x}$

⇒ $x=\frac{40}{\tan 18}$

⇒ $x=\frac{40}{0.325}$

⇒ 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, $\sin\theta=\frac{opposite}{hypotenuse}$

⇒ $\sin 64=\frac{x}{300}$

⇒ $x=300\times \sin 64$

⇒ $x=300\times 0.898$

⇒ 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, $\tan \theta=\frac{opposite}{adjacent}$

⇒ $\tan 12=\frac{45}{x}$

⇒ $x=\frac{45}{\tan 12}$

⇒ $x=\frac{45}{0.213}$

⇒ x = 211.27 m.

Thus, the distance covered by the diver to reach the wreckage is 211.27 meters.