60 degrees,60 degrees,4cm Do the following conditions make a unique triangle, more than one triangle or no triangle possible?

1 answer:

5 0

NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹

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Option C

<u> Answer: </u>

The equation in slope intercept form is $-\frac{5}{12} x-\frac{11}{12}$

The slope is $-\frac{5}{12}$ and y-intercept is $-\frac{11}{12}$

<u>Solution: </u>

The slope - intercept form equation of line is given as

y = mx + c ---- eqn(1)

Where m is the slope of the line. The coefficient of “x” is the value of slope of the line.

c is the y – intercept which is the value of y at the point where the line crosses the y-axis

From question, given that -5x - 12y = 11 --- eqn (2)

On converting equation (2) in slope – intercept form, that is adding 5x on both sides,

-5x - 12y + 5x = 5x + 11

-12y = 5x + 11

Now on dividing -12 on both sides,

$y=-\frac{5}{12} x-\frac{11}{12}$ ---- eqn (3)

Comparing the given equation (3) with equation (1), we get

$m = -\frac{5}{12}$ and $c = -\frac{11}{12}$

Hence Option C is correct.

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Answer:

2np + p²

Step-by-step explanation:

The general formula for the area of a square is A = s², where s = the length of one side of the square. In the case of the smaller square the area would be: n x n = n². Since the side of the larger square is 'p' inches longer, the length of one side is 'n + p'. To find the area of the larger square, we have to take the length x length or (n +p)².

Using FOIL (forward, outside, inside, last):

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Since the area of the first triangle is n², we can subtract this amount from the area of the larger square to find out how many square inches greater the larger square area is.

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Step-by-step explanation:

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