Trigonometry (two dimension)

Question

In triangle ABC, ∠BCA = 90°, BC = 10 cm, AC= p cm and AB = q cm. Given that ∠BAC > 45° Write down a possible value of p and Given that ∠BAC > 30° Write down a possible value of q.

Answer 1

p is the side adjacent to angle A and q is the hypotenuse.

 

If angle A is 45 degrees then so is angle B, since angle C is given as a right angle and

the angle sum of a triangle is 180 degrees.  Therefore triangle ABC is isosceles

and so BC=AC=p=10cm.

 

If angle A is 30 degrees, then you can use the fact that if a right triangle has

a 30 degree angle then the sides in ratio   opposite:hypotenuse:adjacent   is  1:2:sqrt3

So q/10=2/1 implying q=20cm.