Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, how far is Hailey's diving partner from the boat? (round to nearest whole number)
a. 300 ft
b. 313 ft
c. 325 ft
d. 326 ft ****
Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, how far is Hailey's diving partner from the boat? (round to nearest whole number)
a. 300 ft
b. 313 ft
c. 325 ft
d. 326 ft
The correct answer for the usatestprep would be letter B because Hailey's depth is x = 300sin30 = 150 then her partner's depth 150 + 25 = 175. Using that you'll have to then, find horizontal distance which is 3002 = 1502 + b2 and b = 15 . Then, c2 = (1503)2 + (175)2c = 313.25
sinΘ =
opp
hyp
Hailey's depth: x = 300sin30 = 150
partner's depth = 150 + 25 = 175
then, find horizontal distance
3002 = 1502 + b2
b = 150
3
then,
c2 = (150
3
)2 + (175)2
c = 313.25
Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, what is the angle of depression from the boat to Hailey's diving partner? (round to nearest whole number)
To solve this problem, we can use trigonometry and some basic geometry. Let's break down the problem step by step.
First, let's understand the situation. Hailey is scuba diving in the ocean, and her boat is anchored 300 feet away. We are given that the angle of depression from Hailey to the boat is 30°.
Now, we know that Hailey's diving partner is 25 feet directly below her. Our goal is to find the distance between Hailey's diving partner and the boat.
To solve this, we need to create a right triangle with the information given.
Let's assume that Hailey's diving partner is point A, Hailey is point B, and the boat is point C.
We can draw a straight line from point A to point C, representing the distance between the diving partner and the boat. Let's call this line AC.
Next, we draw a straight line from point B to point C, representing the distance between Hailey and the boat. Let's call this line BC.
We can see that angle BAC is a right angle because the diving partner is directly below Hailey.
Now, we know that Hailey's boat is anchored 300 feet away from her. This means that line BC has a length of 300 feet.
We also know that Hailey's diving partner is 25 feet below her, meaning the length of line AB is 25 feet.
We're looking for the length of line AC, the distance between the diving partner and the boat.
To find the length of line AC, we can use trigonometry. The tangent function relates the opposite and adjacent sides of a right triangle. In this case, the opposite side is AB, and the adjacent side is BC.
The tangent of angle BAC is given as 30°. So, we can use the tangent function to find the length of line AC.
tan(30°) = AB / BC
Let's solve for BC, which represents the distance between Hailey and the boat:
BC = AB / tan(30°)
BC = 25 / tan(30°)
Using a scientific calculator, we evaluate the tangent of 30°, which equals approximately 0.5774.
BC = 25 / 0.5774
BC ≈ 43.30 feet
Therefore, the distance between Hailey's diving partner and the boat (line AC) is approximately 43.30 feet.
Rounding it to the nearest whole number, the answer is 43 feet.
Therefore, the correct option is not listed.
Assuming the 300 ft is the direct distance, (hypotenue),
let the horizontal distance be x
cos30 = x/300
x = 300cos30
Hailey's vertical depth:
y/300 = sin30
y = 300sin30 = 150
So partner's depth = 150+70 = 220 ft
partner's distance form boat: z
z^2 = x^2 + y^2
etc