Triangle ABC, right angle at B,side AB=6cm and BC=8cm. D is the mid point of AC, length of BD is ?
a.) 10cm b.) 4cm
c.) 3cm
d.) 5cm
Answers
Answer:
option b is the right answer
Answer:
4 cm
Step-by-step explanation:
This question is testing on the Pythagoras theorem and the sine rule
We have been told that side B is right angled meaning AC is the hypotenuse of this triangle
The formulae for finding the hypotenuse is
C² = B² + A²
Where C is the hypotenuse and A and B are the sides
C² = 6² + 8²
36 + 64 = 100
C² = 100
C = √100
C = 10 cm
We have all the sides and an angle we can therefore use the sine rule to get any angle in the triangle.
Sine rule is as follows
a/sineA = b/sineB = c/sin C = 2R
We are interested in angle C in this case therefore
10/sine 90° = 6/sine C
Sine 90° = 1
10 ÷ 1 = 6/sine C
10 = 6 ÷ sine C
Sine C = 6 ÷ 10
Sine C = 0.6
To get angle C we find the sine inverse of 0.6
C = 36.87°
We have angle c but we have been told the hypotenuse is divided into two equal at D
The line extends to angle B into two equal halves this forms a new triangle
DBC
We want to get line BD we still apply the sine rule
5/sine 45° = c/sine 36.87
Sine 45 = 0.7071
5 ÷ 0.7071 = 7.07106
7.07106 = c/sine 36.87
7.07106 = c / 0.6
C = 7.071 × 0.6
C = 4.2 cm
We round off to get 4 cm
I will attach a photo so you can understand better
