Answer:
The height of the kite with respect to the ground is 46.84 meters.
Step-by-step explanation:
1. Illustrate the problem as a right triangle.
Say that the string is the hypothenuse of a right triangle. The angle (42°) is the elevation of this hypothenuse with respect to the bottom side of the triangle. Hence, the height of the kite from the ground can be found by finding the height of the vertical side of the triangle. Check attached image 1 below to have a better understanding of this problem.
2. Name the angles and sides.
For this problem, we are going to apply the law of sines. For this, we'll have to first name all the angles and sides. These are the rules for naming:
Name the angles with any capital letter. Then, the side that's opposite from that angles will be names with the same letter but in lower case. Check attched image 2 to see how we named the angles and sides of this triangle. Also, check out the law of sines statement in the attached image 3.
3. Find the equation for side b.
Now, let's set our equation to find the height (side b). According to the law of sines, this should be our equation:
[tex]\frac{70}{sin(90)} =\frac{b}{sin(42)}[/tex]
4. Solve the equation for b.
[tex]\frac{70}{sin(90)}*sin(42) =b[/tex] --> Multiply by sin(42°) on both sides of the equation.
[tex]b=\frac{70}{sin(90)}*sin(42)[/tex]--> Reorganize the equation.
[tex]b=46.84m[/tex]
5. Conclusion.
The height of the kite with respect to the ground is 46.84 meters.
