Question

Suppose a rope is nailed to a pole 35 meters above the ground and extended away from the base of the pole. The distance from the base of the pole to the end of the rope is 15 meters. What is the angle made by the rope and the ground?

A. 21.2∘
B. 66.8∘
C. 25.4∘
D. 64.6∘

Answer 1

`B. \: \boxed{66.8}`

Explanation:

`to \: solve \: this \: little \: poblem : we \:apply \: the \: pythagrean \: rule \to \\ \boxed{SOH} \boxed{CAH} \boxed{TOA} \to \\ we \: are \: been \: given : \to \\ the \: \boxed{opp }\: of \: the \: required \: angle \: = 35. \\ the \: \boxed{adj }\: of \: the \: required \: angle \: = 15. \\ now \: lets \: apply \: \boxed{TOA}\to \: \tan( \theta) = (opp)/(adj) \to\\ \tan( \theta) = (opp)/(adj) = (35)/(15) = 2.3333333333 \\ \theta = \tan {}^( - 1) (2.3333333333) \\ \boxed{\theta = 66.80}`

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