Answer:
obtuse
Step-by-step explanation:
A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...
f = a² +b² -c²
And the interpretation is ...
- f > 0 . . . acute
- f = 0 . . . right
- f < 0 . . . obtuse
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<h3>form factor</h3>
For the given side lengths, the form factor is ...
f = 11² +15² -20² = 121 +225 -400
f = -54
<h3>interpretation</h3>
The value is less than zero, signifying an obtuse triangle.
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<em>Additional comment</em>
The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.
This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.
The answer is number B. 2 -9
Answer:
The boat is 33 feet long
Step-by-step explanation:
* Lets explain how to solve the problem
- The scale factor is a ratio between the drawing length and the
actual length
- The two terms of the ratio must have the same unit, then the two
terms of the scale factor must have the same units
* Lets solve the problem
- The scale drawing is 2 inches : 5 feet
∵ 1 foot = 12 inches
∴ 5 feet = 5 × 12 = 60 inches
∴ The scale drawing is 2 : 60
- Simplify it by dividing each term by 2
∴ The scale factor is 1 : 30
∵ The length of the model boat is 13.2 inch
∴ 1 : 30
13.2 : actual length
- By using cross multiplication
∴ The actual length = (13.2 × 30)/1 = 396 inches
∵ The actual length is 396 inches
∵ 1 inch = 1/12 feet
∴ The actual length of the boat = 396 × 1/12 = 33 feet
* The boat is 33 feet long
Answer:
Step-by-step explanation:
(a) For x below 40, the number of miles per hour below 40 is (40-x). Then the fine for that speed is 15(40 -x).
For x between limits, the fine is zero.
For x above 65, the number of miles per hour above 65 is (x-65). Then the fine for that speed is 15(x -65).