Question

A)
Given that
is a Pythagorean triple, which of the following is also a Pythagorean triple?
(1 point)
(5, 12, 13)
(
4
,
11
,
12
)
(
15
,
36
,
39
)
(
10
,
24
,
25
)
(
7
,
14
,
15
)
A)
You go ziplining with your family. There are two platforms, different in height, and you ride on a cablefrom one to the next. You are waiting to go from the taller platform to the lower platform. Horizontally,the platforms are 258 feet apart. The zipline is 450 feet long. Using the inverse of sine, what is theapproximate angle of depression you will travel as you ride the zipline?
(1 point)
35°
90°
65°
55°

Answer 1

Question 1:
Check a^2 + b^2 = c^2.
- (5,12,13): 25 + 144 = 169 = 13^2 → yes.
- (4,11,12): 16 + 121 = 137 ≠ 144 → no.
- (15,36,39): 225 + 1296 = 1521 = 39^2 → yes (3×(5,12,13)).
- (10,24,25): 100 + 576 = 676 ≠ 625 → no.
- (7,14,15): 49 + 196 = 245 ≠ 225 → no.

So the Pythagorean triples here are (5,12,13) and (15,36,39). If one choice is required (scaled from the given triple), pick (15,36,39).

Question 2:
Horizontal = 258 (adjacent), hypotenuse = 450. Vertical = sqrt(450^2 − 258^2) ≈ 368.7. Angle of depression θ = arcsin(vertical/hypotenuse) = arcsin(368.7/450) ≈ 55°. So choose 55°.