Posted by Lee Pearce on Sunday, June 20, 2010 at 8:03am.
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.
thank u
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.
Related Questions
math - Triangle ABD in the diagram has a right angle A and sides AD = 4.9cm and ...
Math(Geometry) - In the diagram below(no diagram but details will be provided), ...
Geometry PLEASE HELP ME - What is the range of possible values for x? The ...
Angle question - Quadrilateral JKLM is a rhombus. If mangleLMK = 36, find ...
math - a triangle,side ac is 3/5 of side ab,and is 23.1 m. side ab is 7/9 of ...
maths-constructions - Construct a rhombus ABCD in which AB= 6 cm and angle ABC= ...
MATH!!! - given isosceles triangle ABC, line AB = BC, and BD is the angle ...
Geometry- how to write proof - ABC is a right triangle. Angle C is 90 degree. ...
trig - ABC- with angles AB, and C and sides AB,BC, and AC, angle B is right ...
help math - In triangle ABC, points D,E,F are on sides BC,CA,AB respectively ...
For Further Reading
