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Question
Given A Right angled triangle with sides 3,4 and 5 units. show that one of its angles is 37 degree.

The first thing to do is to confirm that the lengths of the sides correspond to a right triangle. How would you do this? (Hint: Pythagoras' Thm.).

For a right triangle, we have the trigonometric relations

cos(angle) = side adjacent/hypoteneuse and sin(angle) = side opposite/hypoteneuse.

I assume you have drawn the triangle already and can see that we can define

hypoteneuse = 5, side adjacent = 4 and side opposite = 3.

Now to calculate an angle, we need to use the inverse trigonometric functions

cos^1(4/5) = sin^1(3/5) = 37 degrees.

Randy
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 8 Politeness = 10 Comment In fact I actually wanted to know how actually we could get the angle 37 degree without using the inverse of sine, cosine etc.

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography