Engineering

posted by .

Triangle ABD in the diagram has a right angle A and sides AD = 4.9cm and AB = 7.0cm. side AB is extended to C so that ABC is a straight line.
a) use pythagoras theorem in triangle ABD to find the length of BD.
b)use trigonometry in triangle ABD to find angle ABD. hence find angle DBC.
c)angle BCD=21* use the sine formula in triangle BCD to find the length of CD
d)use the cosine formula in triangle BCD to find the length of BC

  • geometry/trigonometry -

    a. Pythagoras theorem
    BD²=AD²+AB²
    AD and AB are known.
    Solve for BD.

    b. Tan(∠ABD) = opposite/adjacent = DA/AB
    Solve for ∠ABD.
    Since ∠ABD and ∠DBC form a straight line, they are supplementary (add up to 180°).
    Solve for ∠DBC:
    ∠DBC = 180 - ∠ABD

    c. Sine rule
    The sine rule applies when all angles are known plus one side, or two sides are known and one angle which is not the included angle.
    The given triangle applies in to the first case.
    BD, ∠DBC, ∠BCD are known, so apply the sine rule:
    a/sin(A)=b/sin(B)=c/sin(C)
    where A is the angle opposite side a, etc.
    BD/sin(∠BCD)=DC/sin(∠DBC)
    Solve for DC.

    d. The cosine rule applies when two adjacent sides and the included angle are known.
    By now, BD, DC and ∠BDC are known.
    Note: ∠BDC = 180-(∠DBC+∠BCD)
    So apply the cosine rule to solve for c
    c²=a²+a²-2abcos(C)
    or
    BC²=BD²+CD²-2 BD CD cos(∠BDC)

    Post to check your results if you wish.

  • Engineering -

    thank u

  • geometry/trigonometry -

    Triangle ABC is similar to triangle APQ with angle CBA equal to angle QPA and angle A common to both triangles. the length of sides AB, AP and PQ are 90cm,60cm and 30 cm. calculate the length of the side BC.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geomentry

    What is the converse of the theorem statement: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If two sides of a triangle are divided in the same proportion, …
  2. pls help w/t math ?

    in a right triangle ABC, if ab is 14 and bc is 12 wut is bd?
  3. math

    Triangle ABD in the diagram has a right angle A and sides AD = 4.9cm and AB = 7.0cm. side AB is extended to C so that ABC is a straight line. a) use pythagoras theorem in triangle ABD to find the length of BD. b)use trigonometry in …
  4. Math(Geometry)

    In the diagram below(no diagram but details will be provided), right triangle ABC and line BD is an altitude to side line AC. * Prove that (AB)^2=(AC)(AD) -When you label the triangle B should be were the right angle is C should be …
  5. Geometry

    Please answer at least one . PLEASE 1. Triangle XYZ has a right angle at Y. V,W are on XZ such that XV=XY. WZ=YZ, find ANGLE VYW . 2. STUVWXYZ is a regular octagon. Find SW/ TZ. 3. The interior angles of a convex polygon form an arithmetic …
  6. Geometry

    Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD?
  7. geometry

    Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD?
  8. Math

    ∆ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices. The measure of the longest side of ∆ABC is units. ∆ABC is triangle. If ∆ABD is formed with the point D(1, 2) as its third vertex, then ∆ABD …
  9. math

    The base (BC) of an isosceles triangle (ABC) is also the side of a square (BCEF) in which the triangle is inscribed. A perpendicular line is drawn in the triangle from B to AC at D, forming triangle ABD. What is the ratio of triangle …
  10. Geometry

    1. If RST=NPQ, which of the following is true?

More Similar Questions