Karan and his sister Riddhima visited at their uncle’s place-Bir, Himachal Pradesh. During day time Karan, who is standing on the ground spots a paraglider at a distance of 100 m from him at an elevation of 30°. His sister Riddhima is also standing on the roof of a 20 m high building observes the elevation of the same paraglider as 45°. Karan and Riddhima are on the opposite sides of the paraglider. Based on the above information, answer the following questions. i. Make a labelled figure on the basis of the given information and calculate the distance of paraglider from the ground. 4 ii. Calculate the distance between the paraglider and the Riddhima. What is the angle of elevation if the distance between paraglider and Karan becomes half of the previous distance
Answers
Answer:
Explanation:
I There is a 50-meter gap between the paraglider and the earth.
ii) The paraglider is 30 metres away from Riddhima.
Given:-
Karan is 100 metres away from the paraglider, and the elevation angle is 30 degrees.
The paraglider and Riddhima are 45° apart in elevation. She is 20 metres in the air.
Both of them are on different sides of the paraglider.
To Locate:
I The paraglider's separation from the ground
ii) The separation between Riddhima and the paraglider
Solution:-
I Assign three points in the DQA to Karan, the paraglider, and the ground.
In ΔDQA,
Sin30 = DQ/AD
∴DQ/100 = 1/2 (Sin30 = 1/2)
⇒DQ = 100/2
⇒DQ = 50m
50 metres separate the paraglider from the ground.
ii) We are aware that the separation between the ground and and the paraglider is 50m, and we are also aware that Riddhima is 20m from the earth. As a result, there will be a significant variation between the paraglider and Riddhima.
⇒50m - 20m = 30m
Let the height we just attained and the distance between Riddhima and the paraglider be the points in the triangle DPB.
In ΔDPB,
Sin45 = DP/DB
30/DB =1/
DB=30
∴The paraglider is 30 metres away from Riddhima.
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