A ladder on the platform of a fire brigade van can be elevated at an angle of 70°
Chapter 6 – Trigonometry – Text Book Solution
Problem set 6| Q 9| Page 139
A ladder on the platform of a fire brigade van can be elevated at an angle of 70° to the maximum. The length of the ladder can be extended upto 20m. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach. (sin 70° = 0.94)
Solution
Let the maximum height from the ground upto which the ladder can reach be h meters.
Using the concept of trigonometry, we have:
sin 70° = opposite/hypotenuse
or, hypotenuse = opposite/sin 70°
or, hypotenuse = h + 2/0.94 (as the platform is 2m above the ground)
or, hypotenuse = (h + 2)/0.94
Now, the length of the ladder is given as 20m, so we can write:
hypotenuse = 20/cos 70° (using the concept of trigonometry)
or, (h + 2)/0.94 = 20/cos 70°
or, h + 2 = 0.94 x 20 / cos 70°
or, h = 0.94 x 20 / cos 70° – 2
Evaluating this expression using a calculator or by looking up the value of cos 70° as 0.342, we get:
h ≈ 21.76 meters (rounded to two decimal places)
Therefore, the maximum height from the ground upto which the ladder can reach is approximately 21.76 meters.
Chapter 6 – Trigonometry – Text Book Solution
Problem Set 6 |Q 9| P 139
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