Question
(a) Find the value of x in the below diagram given that, ∠ACB = 25o, ∠CBA = 15o and CD is the height of C from the extended line segment BA:
(b) The lengths of two sides of a triangle are 13 cm and 16 cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. Find the value of a + b? [4 MARKS]
Answer: Option A
:
Each part: 2 Marks
In the given triangle ABC,
(a) Sum of all angles of a triangle = 180o
Or, ∠CAB + ∠ABC + ∠BCA = 180o
Or, ∠CAB + 15o + 25o = 180o
Or, ∠CAB = 180o - 40o = 140o
For the triangle ACD,
∠D + X = ∠CAB (∵ sum of interior opposite angles = exterior angle)
90o + X = 140o (∵ CD is an altitude from C to extended BA, ∴ ∠D = 90o)
Or, X = 50o
(b) The third side of a triangle must be greater than the difference between the other two sides.
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:
Each part: 2 Marks
In the given triangle ABC,
(a) Sum of all angles of a triangle = 180o
Or, ∠CAB + ∠ABC + ∠BCA = 180o
Or, ∠CAB + 15o + 25o = 180o
Or, ∠CAB = 180o - 40o = 140o
For the triangle ACD,
∠D + X = ∠CAB (∵ sum of interior opposite angles = exterior angle)
90o + X = 140o (∵ CD is an altitude from C to extended BA, ∴ ∠D = 90o)
Or, X = 50o
(b) The third side of a triangle must be greater than the difference between the other two sides.
That is, third side > (16 - 13) which is 3 cm.
Also, Sum of lengths of any two sides of a triangle is always greater than the third side.
i.e., third side < (16+13) which is 29 cm.
Hence, a + b = 3 + 29 = 32.
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