length of the trail??

Geometry Level 3

A straight trail with a uniform inclination of 15° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 8500 feet. What is the length of the trail(to the nearest foot)?

20,751 ft 31,751 ft 19,751 ft 39,751 ft 69,751 ft 29,751 ft 23,751 ft

Aditya Raj by Aditya Raj , 22, India

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2 solutions

Consider the diagram on the left.

sin ⁡ 15 = 7700 t \sin 15=\dfrac{7700}{t}

t = 770 sin ⁡ 15 ≈ t=\dfrac{770}{\sin 15}\approx 29.751 f e e t \boxed{29.751~feet}

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Aditya Raj
Feb 26, 2015

A straight trail with a uniform inclination of 15° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 8500 feet. What is the length of the trail(to the nearest foot)?

Draw a right triangle with the trail as the hypotenuse=x

The side opposite the 15˚ angle=8500-800=7700 sin15˚=x/7700 x=7700/sin15˚=29751 length of the trail=29,751 ft

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Please set a suitable level for your problems. In this case, this is just setting up a right angle trigonometry, and the hardest part is evaluating sin ⁡ 1 5 ∘ \sin 15 ^ \circ . It is certainly not a level 5 problem, and is much closer to level 2-3.

Calvin Lin Staff - 6 years, 3 months ago

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ok sir i will take care of it...

Aditya Raj - 6 years, 3 months ago

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