Question

In a right-angled triangle
smallest angle : largest angle = 3:5
Work out the three angles of the triangle.
Your final line should be written like this. The angles are ... , ... , ...

Answer 1

Answer: $36^{\circ}, 54^{\circ}, 90^{\circ}$

Step-by-step explanation:

Given

Triangle is right-angled

The ratio of smallest and largest angle is 3:5

let the angles be 3x and 5x

In a right-angled triangle, the largest angle is $90^{\circ}$

$\therefore5x=90^{\circ}$

$x=\frac{90^{\circ}}{5}=18^{\circ}$

3x is the smallest angle. Its complementary angle is $90^{\circ}-3x=90^{\circ}-3\times18^{\circ}$

Complementary angle is $36^{\circ}$

$3x=54^{\circ}$

$5x=5\times18^{\circ}=90^{\circ}$