MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer:7, and 7√2Step-by-step 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 have6x = 180 x = 30Each 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