PLEASE HELP WITH A FEW QUESTIONS

triangle ABC has side lengths 8, 15, and 17 do the side lengths form a pythagorean triple?

the length of the hypotenuse of a 30-60-90 triangle is 7 find perimeter

to approach the runway, a pilot of a small plane must begin a 10descent starting from a height of 1,790 feet above the ground to the nearest tenth of a mile how many miles from the runaway is the airplane at the start of this approach
my answer 0.3mi

a glider lands 18miles west and 5 miles south from where it took off the result of the trip can be described by the vector(-18,-5)use distance(magnitude)and direction to describe this vector a second way.
i know it's south of west but not sure of the miles

Its crazy how this was question 10 years ago these dudes are probably fathers now

1. a = 8.

b = 15
c = 17.

c^2 = 17^2 = 289.
a^2 + b^2 = 64 + 225 = 289 = c^2.
Answer: Yes.

2. Z = 7 = hyp.
X = 7*cos30 = 6.06 = hor. side.
Y = 7*sin30 = 3.5 = ver. side.
P = 7 + 6.06 + 3.5 = 16.56.

3. We form a rt triangle:
X = -18 Miles = Hor. side.
Y = -5 Miles = Ver. side.
Z = Hyp.

tanAr = Y/X = -5 / -18 = 0.27777.
Ar = 15.5 Deg. = Reference angle.
A = 180 + 15.5 = 195.5 Deg., CCW.
Z = X/cosA = -18 / cos195.5=18.7 Miles
= Magnitude.
Direction = 195.5 Deg. CCW = 15.5 Deg.
South of west.

ikr

what is the answer to this question?

Sorry, which question are you referring to? Please provide more information.

Sure, I can help with your questions.

1. To determine if the side lengths 8, 15, and 17 form a Pythagorean triple, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, if 8, 15, and 17 are the side lengths of a right-angled triangle, then we have to check if 8^2 + 15^2 = 17^2 holds true. Evaluating this equation, we find that 64 + 225 = 289, which is indeed true. Therefore, the side lengths 8, 15, and 17 form a Pythagorean triple.

2. A 30-60-90 triangle is a special type of right triangle in which the angles measure 30 degrees, 60 degrees, and 90 degrees. In such a triangle, the length of the hypotenuse is always twice the length of the shorter leg, and the length of the longer leg is (√3)/2 times the shorter leg. In this case, the length of the hypotenuse is given as 7. Therefore, the length of the shorter leg is 7/2, and the length of the longer leg is (√3/2) * (7/2). To find the perimeter, we add up the lengths of all the sides. P = shorter leg + longer leg + hypotenuse = (7/2) + (√3/2) * (7/2) + 7. Simplifying this expression, we get the perimeter as the final answer.

3. To determine the distance from the runway, you can use the fact that the plane descends from a height of 1,790 feet to the ground. First, convert the descent height to the same unit as the answer you are looking for, which is miles. Since 1 mile is equivalent to 5,280 feet, divide 1,790 by 5,280 to convert it to miles. This would give you the approximate distance in miles from the start of the approach to the runway.

4. The vector (-18, -5) represents the displacement of the glider, where the first component (-18) represents the displacement in the west direction, and the second component (-5) represents the displacement in the south direction. To find the distance (magnitude) of the displacement, you can use the Pythagorean theorem again. Since the vector (-18, -5) forms a right-angled triangle with the west and south directions, the magnitude of the displacement is given by the square root of the sum of the squares of the components, i.e., √((-18)^2 + (-5)^2). Evaluating this expression would give you the distance in miles. To describe the direction, you can use the angle between the displacement vector and the reference direction (such as east or north). You can use trigonometry to find this angle.

stoopid