ar44167
Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Let △ABC be a right triangle with m∠C = 90°. Given tan ∠A = 0.25, find tan ∠B.

Sagot :

Answer:  4

==========================================================

Rule:

If A+B = 90, then tan(A) = 1/( tan(B) ) and tan(B) = 1/( tan(A) )

-------

Since C = 90, this must mean the other two angles A and B are acute and complementary. So A+B = 90 must be the case. This allows us to use that rule above.

So,

tan(B) = 1/( tan(A) )

tan(B) = 1/( 0.25 )

tan(B) = 4

-------

Here's another way to think about it.

If tan(A) = 0.25, then we could have BC = 1 and AC = 4 as the opposite and adjacent sides respectively. That leads to tan(A) = opposite/adjacent = BC/AC = 1/4 = 0.25

When computing tan(B), the BC and AC sides swap roles in terms of opposite and adjacent,

tan(B) = opposite/adjacent = AC/BC = 4/1 = 4.

For any of these cases, we don't involve the hypotenuse AB.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.