Jasmine is flying a kite. She lets out 86 feet of string. She takes the kite into the ground and measures the angle. The string forms a 47° angle with the ground. Which expression could be used to determine how high above the ground the kite is flying?
A) 86 cos 47°
B) 86 sin 47°
C) cos 47°/86
D) sin 47°/86
If we draw a picture of a right triangle where the hypotenuse (longest side) is the 86ft of string and the height of the kite of the ground is directly opposite to the given angle of 47°, then we use the sine function where sin(θ)=opposite/hypotenuse
Therefore, sin(47°)=x/86 will be the equation to determine the height of the kite from the ground. Solving for x, the height, we get x=86sin(47°), which makes option B correct.
Well, aren't we flying high with this question! To determine how high above the ground the kite is flying, we can use the sine function since it relates the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Therefore, the expression that could be used is option B) 86 sin 47°. Keep reaching for the sky, Jasmine!
The expression that could be used to determine how high above the ground the kite is flying is option B) 86 sin 47°.
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the length of the side opposite the angle (height of the kite above the ground) is what we want to find, and the length of the hypotenuse is the length of the string, which is 86 feet.
So, using the sine function, we can express the height of the kite above the ground as 86 sin 47°.
To determine how high above the ground the kite is flying, we need to use trigonometry since we have the length of the string and the angle formed with the ground.
The trigonometric function used to relate the angle and the sides of a right triangle is the sine function (sin). The sine of an angle is defined as the opposite side divided by the hypotenuse, and in this case, the height of the kite is the opposite side, and the length of the string is the hypotenuse.
So, the expression that could be used to determine how high above the ground the kite is flying is:
B) 86 sin 47°