To solve this problem, we need to use the concept of trigonometry. Here, we are given the length of the hypotenuse (the kite string), the angle it makes with the horizontal, and the height from which it is held. We are asked to find the altitude of the kite, which is the opposite side in our right triangle.

The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, we are given that cos θ = 1/3. However, we need the sine of the angle to find the opposite side (the altitude of the kite).

Since sin² θ + cos² θ = 1, we can find sin θ by taking the square root of (1 - cos² θ).

So, sin θ = sqrt(1 - (1/3)²) = sqrt(1 - 1/9) = sqrt(8/9) = 2sqrt(2)/3.

Now, we can find the length of the opposite side (the altitude of the kite from Jof's hand) by multiplying the length of the hypotenuse by sin θ.

Altitude from Jof's hand = 35m * 2sqrt(2)/3 = 70sqrt(2)/3 m.

However, we are asked for the total altitude of the kite from the ground. Since Jof is holding the string 1 meter above the ground, we need to add this to our calculated altitude.

Total altitude of the kite = 70sqrt(2)/3 m + 1m.

Question

To solve this problem, we need to use the concept of trigonometry. Here, we are given the length of the hypotenuse (the kite string), the angle it makes with the horizontal, and the height from which it is held. We are asked to find the altitude of the kite, which is the opposite side in our right triangle.

The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, we are given that cos θ = 1/3. However, we need the sine of the angle to find the opposite side (the altitude of the kite).

Since sin² θ + cos² θ = 1, we can find sin θ by taking the square root of (1 - cos² θ).

So, sin θ = sqrt(1 - (1/3)²) = sqrt(1 - 1/9) = sqrt(8/9) = 2sqrt(2)/3.

Now, we can find the length of the opposite side (the altitude of the kite from Jof's hand) by multiplying the length of the hypotenuse by sin θ.

Altitude from Jof's hand = 35m * 2sqrt(2)/3 = 70sqrt(2)/3 m.

However, we are asked for the total altitude of the kite from the ground. Since Jof is holding the string 1 meter above the ground, we need to add this to our calculated altitude.

Total altitude of the kite = 70sqrt(2)/3 m + 1m.

Knowee AI · Accepted Answer

To solve this problem, we need to use the concept of trigonometry. Here, we are given the length of the hypotenuse (the kite string), the angle it makes with the horizontal, and the height from which it is held. We are asked to find the altitude of the kite, which is the opposite side in our right triangle.

The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, we are given that cos θ = 1/3. However, we need the sine of the angle to find the opposite side (the altitude of the kite).

Since sin² θ + cos² θ = 1, we can find sin θ by taking the square root of (1 - cos² θ).

So, sin θ = sqrt(1 - (1/3)²) = sqrt(1 - 1/9) = sqrt(8/9) = 2sqrt(2)/3.

Now, we can find the length of the opposite side (the altitude of the kite from Jof's hand) by multiplying the length of the hypotenuse by sin θ.

Altitude from Jof's hand = 35m * 2sqrt(2)/3 = 70sqrt(2)/3 m.

However, we are asked for the total altitude of the kite from the ground. Since Jof is holding the string 1 meter above the ground, we need to add this to our calculated altitude.

Total altitude of the kite = 70sqrt(2)/3 m + 1m.

3. Jof is holding the rear end of a kite string 1 meter above the ground. If the kite string is 35 meters long and makes an angle with the horizontal, and cos θ=1/3 . What is the altitude of the kite?

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