Triangle LMG has side lengths of 7cm, 24 cm, and 25 cm. Which type of triangle is LMG?
a.right <--- or b?
b.obtuse
c.acute
d.equilateral
Bethel Park is 28 miles directly west of Jeanette and 10.3 miles directly south of Pittsburgh. Which is the length of the road that runs straight from Pittsburgh to Jeanette?
26 miles
29.8 miles
25 miles<-- or d?
33.4 miles
Your first answer (a) is right; the second is wrong.
it's actually 29.8 miles
For the first question, we have a triangle with side lengths of 7 cm, 24 cm, and 25 cm. To determine the type of triangle it is, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.
So, let's calculate:
7^2 + 24^2 = 49 + 576 = 625
25^2 = 625
Since both sides are equal, the triangle satisfies the Pythagorean theorem and is a right triangle. Therefore, the correct answer is a) right.
For the second question, we have the locations of Bethel Park, Jeanette, and Pittsburgh. To find the length of the road that runs straight from Pittsburgh to Jeanette, we can use the distance formula based on their coordinates.
Let's assume Pittsburgh's coordinates are (0, 0), and Jeanette's coordinates are (x, y). According to the problem, Jeanette is 10.3 miles directly south of Pittsburgh, so the y-coordinate of Jeanette is -10.3.
Also, it is stated that Bethel Park is 28 miles directly west of Jeanette. So, the x-coordinate of Jeanette would be -28.
Now, we can calculate the distance using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-28 - 0)^2 + (-10.3 - 0)^2)
Distance = sqrt((-28)^2 + (-10.3)^2)
Distance = sqrt(784 + 106.09)
Distance = sqrt(890.09)
Distance ≈ 29.8 miles
Therefore, the correct answer is b) 29.8 miles.