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Question

(a) Find x in the below diagram. What are such triangles called?




(b) In a triangle ABC, an altitude is dropped from A to BC at D. A=40,B=(2x+4),C=(4xk),BAD=30
Find k , x and the values of the angles. [4 MARKS]


Solution

(a) Solution: 1 Mark
     Type of triangle: 1 Mark
(b) Solution: 1 Mark
     Correct answer: 1 Mark


(a) For a triangle, sum of all angles = 180o
Or, (2x - 15o) + (x + 20o) + (x + 15o) = 180o
Or, 2x + x + x - 15o + 20o + 15o = 180o
Or, 4x + 20o = 180o
Or, 4x = 160o
Or, x = 1604 = 40o

The angles of the triangle will be, (2x - 15o = 65o), (x + 20o = 60o) and (x + 15o = 55o)
Since all angles are less than 90o, it's an 'acute angled triangle' and also all the angles are of different values therefore all the sides will be of different length, hence it is a 'scalene triangle'.


(b
             

In triangle ABD
2x+4+90+30=180
2x=180124
x=562
x=28

In triangle ADC
4xk+90+10=180
4xk=180100
4(28)k=80 (Substituting the value of x=28)
k=4(28)80
k=11280
k=32

The angles are 40,60 and 80 for the given triangle.

Mathematics

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