Question

If two acute angles of a right angled triangle are in the ratio 7:8, find these angles

Answer 1

lab one of the acute angle be 7x
and the other being 8x...
since the other angle is 90 degree we can say that these two acute angles are complementary (180-90)
so. 8x+7x=90
15x=90°
x=6
... so the first angle will be (7*6)=42°
and the other angle will be (8*6)=48°

Answer 2

It is given that the triangle is right-angled.
So, one angle is 90 degree.
Let the other two angles be 7x and 8x.
According to Angle Sum Property , the sum of the three angles of a triangle is 180 degree.
So, 7x+8x+90 = 180
= 15x+90 = 180
= 15x = 180-90
= 15x = 90
= x = 90/15
= x = 6
First angle = 90 degree.
Second angle = 7x = 7*6 = 42 degree
Third angle = 8x = 8*6 = 48 degree

Substitution
90+42+48 = 180
= 180 = 180