Casey and Tamary are standing 14 ft. apart from each other and looking up at a kite that is flying between them. Casey is flying the kite on a 70 ft. string at an angle of 72 degrees with the ground. How far is Tamary from the kite?
a. 73.1 ft.
b. 67.0 ft.
c. 75.5 ft.
d. 69.2 ft.
It’s 67 feet option B
mitch carried
Oh boy, looks like Casey and Tamary are having a "stringy" situation! Let's solve this puzzle.
Since Casey is flying the kite on a 70 ft. string and the angle with the ground is 72 degrees, we can use some trigonometry to find the height of the kite.
Now, we all know that triangles can be a little "tri-cky," but luckily we have the sine function to help us out.
So, let's use sine to find the height of the kite. The formula is: sin(angle) = opposite/hypotenuse.
In this case, the opposite side is the height of the kite, and the hypotenuse is the length of the string, which is 70 ft.
Now, we just need to compute sin(72 degrees) = opposite/70 ft.
If we rearrange the equation, we can isolate the opposite side: opposite = sin(72 degrees) * 70 ft.
Calculating this, we find that the height of the kite is approximately 67.0 ft.
Now, since Casey and Tamary are standing 14 ft. apart, we can use the Pythagorean theorem to determine how far Tamary is from the kite.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, Tamary's distance from the kite is the hypotenuse, and we already know the height of the kite and the distance between Casey and Tamary.
Let's call Tamary's distance 'x', so we have: x^2 = 14^2 + 67.0^2.
Calculating this, we find that x is approximately 73.1 ft.
So, the answer is A: 73.1 ft.
Tamary might have to do a little "string" dance to get closer to Casey and the kite!
To find the distance between Tamary and the kite, you can use trigonometry. The given information is the distance between Casey and Tamary (14 ft), the length of the string (70 ft), and the angle that the string makes with the ground (72 degrees). Let's assume that Tamary is on the same horizontal line as Casey.
To find the distance between Tamary and the kite, you can use the sine function. The sine function relates the length of the side opposite an angle in a right triangle to the hypotenuse of the triangle. In this case, Tamary is opposite the angle of 72 degrees, and the hypotenuse is the length of the string (70 ft).
The formula to calculate the opposite side is:
Opposite side = Hypotenuse × sin(angle)
Opposite side = 70 ft × sin(72 degrees)
Using a calculator, you can find that sin(72 degrees) is approximately 0.951.
Opposite side = 70 ft × 0.951
Opposite side ≈ 66.57 ft
Therefore, Tamary is approximately 66.57 ft away from the kite.
Since none of the answer options match this result exactly, you may need to round the answer. The closest option is b. 67.0 ft.
Do we have an answer for this?
the height of the kite is ... 70' sin(72º)
the distance from Casey to directly under the kite is ... 70' cos(72º)
find the distance from Tamary to directly under the kite
... 14' - Casey's distance
use Pythagoras (a^2 + b^2 = c^2) to find Tamary's distance from the kite
Sketch a well labelled diagram.
You will be able to use the COSINE LAW for the length of the unknown side :)
Let me know if you are unable to find one of the answers.
The question worked out very nicely.