What is the length of the side opposite the 30° angle?

Mathematics

1 answer:

Sladkaya [172]3 years ago

8 0

Answer:

5/√3 inches long.

Step-by-step explanation:

The property is that the lengths of the sides of a 30-60-90 triangle are in the ratio 1:2:√3. Thus if you know that the side opposite the 60 degree angle measures 5 inches then then this is √3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long.

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Triangle ABC has sides with lengths of 11, 18, and 8 units. Determine whether this triangle is a right triangle.

Arturiano [62]

Answer:

Not a right triangle.

Step-by-step explanation:

If this triangle is a right triangle, then the Pythagorean theorem would work on it. According to the Pythagorean theorem, $a^2+b^2=c^2$ , so c would always be greater than a or b. In this scenario, the greatest number here is 18, so c = 18. Since a or b don't matter if given both legs, we have the following equation that may or may not be equal: $8^2+11^2=18^2$ . We know 8 squared is 64, and 11 squared is 121, and 18 squared is 324. This means that $64+121=324$ according to the Pythagorean theorem, and since 64 + 121 = 185, and 185 does not equal 324, the Pythagorean theorem does not work and the triangle is not a right triangle.