The hypotenuse of a 30°-60°-90° triangle measures 10 inches. Which could be the length of a leg of the triangle?

Mathematics

1 answer:

diamong [38]3 years ago

4 0

Answer:

6 and 8

Step-by-step explanation:

The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To find the length of one of the legs, we use the idea of Pythagorean Triples.

Pythagorean Triples are any set of three numbers that satisfies the Pythagorean Theorem. Some common examples are:

3, 4 and 5
5, 12 and 13
9, 40 and 41

Note that in a Pythagorean Triple,

The longest length is always the Hypotenuse.
New Triples can be formed from product of existing triples.

In our given triangle, the Hypotenuse=10 Inches

Consider the Pythagorean Triple 3,4, and 5

5 is the Hypotenuse
Multiply the Triples by 2, we obtain:
6, 8 and 10 (in which 10 is the hypotenuse)

Therefore, 6 and 8 could be the length of a leg of the 30°-60°-90° triangle.

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what is the area of the figure ? answers a. 12 units2 b. 17 units 2 c. 16 units 2 d. 24 units2 e. none

stellarik [79]

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Answer:

17 square units

Step-by-step explanation:

There are several ways you can divide this figure into areas that are easily computed.

One that comes to mind is to consider the triangle that would include the missing area at lower right. That triangle would have a base of 6 and a height of 8, so an area of ...

A = (1/2)bh

A = (1/2)(6)(8) = 24 . . . . square units

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Then the area of the shaded part is ...

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A recipe makes 6 2/3 cups. The serving size is 5/6 cup. How many servings does the recipe make?

Dmitry [639]

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3 years ago

Help me please. I don't understand this.

navik [9.2K]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

Apparently, you're being asked to identify the sequence of steps you would use to compute the volume of the pyramid.

It seems to be a good idea to start with the formula for the volume.

Then, recognize that you need to compute B, so make that computation. The area of the base (B) is the product of the base dimensions (14)(12).

Once you have the value of B, then you can put that, along with the value of h, into the original volume formula.

Evaluating it gives the volume in cubic units.

_____

<em>Additional comment</em>

If you're familiar with the pyramid volume formula, you know that you must compute B before you can make use of the formula. That makes the sequence be B=14(12); B=168; V=1/3Bh; V=1/3(168)(7).

However, if you're starting from scratch, it is probably good to begin with the volume formula. That is what tells you that you need to find B in the first place. This is the sequence we show below.