Law of Sines Law of Sines Law of Sines11-4th-9.pptx

Law of Sines
Law of Sines

1. Activity No. Solve Me Directions: Solve the following. 25 x 45 ° 28 15 Ɵ

2. Solving Problems Involving Angle of Depression

3. Learning objectives; At the end of this lesson the students will be able to: solve problems involving angle of depression solve for the missing sides and angles of right triangles using the angle of depression.

4. Examples: Solve the following. 1. An observer lying on the top of a hill in Binangonan , Rizal is overlooking the view of Laguna Lake. Suppose that the hill is 25 meters high, and the angle of depression of the observer to the lakeshore is 64o11’, what is the distance of the lakeshore to the foot of the hill?

5. 2. A cat is seen looking at the window of a building. As the cat looks downward, it saw a garbage can outside. If the window where the cat is seen is 6 meters above the ground and the garbage can is 2 meters away from the base of the building, what is the angle of depression of the cat to the garbage can?

6. Activity 2. Do it your Self! Direction: Solve for the value of x. Give the lengths of the sides in two decimal places. For numbers 3, 4, and 5, solve for θ and give the angle measures in degrees and minutes. 1. 2. x 15 27 ° 25’ A B C x 15 27 ° A B C 19 x 18 ° E F G

7. 27 19 Ɵ H I J 28 17 Ɵ   X Y Z 19 12 Ɵ   L M N 4. 5.

8. Directions: Read each of the following carefully. Choose the letter that corresponds to the correct answer.   From the top of a mountain, 135 meters high, a ship is seen below in the sea. It is observed that the angle of depression of the ship is 21 o . How far is the ship from the top of the mountain? 376.71 𝑚 376 𝑚 376.72 𝑚 376.73 𝑚

9. On the rooftop of a school building, an observer saw a broken chair on the school ground 4 meters away from the base of the building. What is the angle of depression of the observer to the broken chair if the building is 18 meters high? 77 𝑜 38′ C. 77 𝑜 28′ 77 𝑜 18′ D. 77 𝑜 A pilot on a plane saw a nearby island in front of him. If he is 2975 m above the ground and the horizontal distance of the island to the pilot 2345 m away. What is the angle of depression of the pilot to the island? 51 𝑜 45′ C. 51 𝑜 43′ 51 𝑜 40′ D. 51 𝑜

10. A boy is seen standing on the highest part of a mango tree. On top of the tree, he saw an observer looking at him 5 meters away. If the angle of depression of the boy to the observer is 34o26’, what is the height of the tree? 3.44 𝑚 C. 3.42 𝑚 3.4 𝑚 D. 3.43 𝑚 A man is seen on top of a coconut tree. 3 meters away from him is another coconut tree. On the bottom of the other tree, there is a fallen coconut. If the angle of depression of the man to the fallen coconut is 68o17’, how high is the coconut tree that he is located? 7.55 𝑚 C. 7.53 𝑚 8 𝑚 D. 7.5 𝑚