Question

The ratio of the angle measures of a triangle is 1.5: 1.5: 3. The length of the side opposite the smallest angle is 7 inches. Find the lengths of the other two sides of the triangle.

Answer 1

7, and 7√2

Explanation:

The angle ratios are 1.5 : 1.5 : 3, so there are

1.5 + 1.5 + 3 = 6 total parts. There are 180° in a triangle, so we have

6x = 180

x = 30

Each part is 30°,

1.5 becomes 45° (30 plus half of 30)

3 becomes 90°

There are 2 angles with a ratio of 1.5, so we have a 45° - 45° - 90° triangle.

The side opposite the smallest angle is 7, there are angels with the least measure, so there are 2 sides that are 7.

The hypotenuse of a 45° - 45° - 90° triangle is larger than the legs by a factor of √2, so the hypotenuse is 7√2