Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

need help asap?

Consider the triangle ABC with C=90∘. Compute the following trigonometric values when a=1 and b=5.

what does

sinA=

cosA=

sinB=

cosB=

6 Answers

Relevance
  • sepia
    Lv 7
    1 month ago

    Consider the triangle ABC with C = 90∘. 

    Compute the following trigonometric values when a = 1 and b = 5. sin A =cos A =sin B =cos B =

  • 1 month ago

    we 1st need to solve for the hypotenuse by using pythagorean theorem.

    c = √(a^2 + b^2)

    c = √(1^2 + 5^2)

    c = √(26)

    so

     

    sin(A) = 1/√(26) or √(26)/26        

      

    cos(A) = 5/√(26) or 5√(26)/26

    sin(B) = 5/√(26) or 5√(26)/26

    cos(B) = 1/√(26)  or √(26)/26

  • Philip
    Lv 6
    1 month ago

    In triangle ABC, (A,B,C) is opposite (a,b,c) = (small arm,larger arm,hypotenuse)

    Clearly, c^2 = a^2+b^2 = 1^2+5^2 = (rt26)^2, where rt = ''square root of''. Then

    c = rt26.;

    By law of sines, a/sinA = b/sinB = c/sinC;

    c/sinC = rt26/sin90 = rt26/1 = rt26;

    a/sinA = rt26, ie., sinA = a/rt26 = 1/rt26 = (1/26)rt26.;

    b/sinB = rt26, ie., sinB = b/rt26 = 5/rt26 = (5/26)rt26.;

    cos^2(A) = 1 - sin^2(A) = 1 - (1/26) = (25/26). Then cos(A) = (5/26)rt26.;

    cos^2(B) = 1 - sin^2(B) = 1 - (25/26) = (1/26). Then cos(B) = (1/26)rt26.;

  • 1 month ago

    Refer to the figure below.

    c² = a² + b² (Pythagorean theorem)

    c = √(1² + 5²) = √26

    sinA = a/c = 1/√26 = (√26)/26

    cosA = b/c = 5/√26 = 5(√26)/26

    sinB = b/c = 5/√26 = 5(√26)/26

    cosB = a/c = 1/√26 = (√26)/26

    Attachment image
  • How do you think about the answers? You can sign in to vote the answer.
  • ted s
    Lv 7
    1 month ago

    the reference triangle for angle  A is { 5 , 1 , √26 } ...thus sin A = 1 / √26...you certainly can finish

  • Tasm
    Lv 6
    1 month ago

            Sohcahtoa

Still have questions? Get your answers by asking now.