A kite flying in the air has an 11-ft line attached to it. Its line is pulled taut and casts a 10-ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
Question
A kite flying in the air has an 11-ft line attached to it. Its line is pulled taut and casts a 10-ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
Solution
This problem can be solved using the concept of similar triangles. The shadow of the kite, the line attached to the kite, and the line from the top of the kite to the end of the shadow form a right triangle. The height of the kite, the length of the shadow, and the line from the top of the kite to the observer form a similar right triangle.
Here are the steps to solve the problem:
-
Identify the lengths of the sides of the triangles. The length of the line attached to the kite is 11 ft and the length of the shadow is 10 ft.
-
Set up a proportion to find the height of the kite. The height of the kite is to the length of the line (11 ft) as the length of the shadow (10 ft) is to the length of the line (11 ft). This can be written as: height/11 = 10/11.
-
Solve the proportion for the height. Multiply both sides of the equation by 11 to solve for the height: height = 11 * (10/11) = 10 ft.
So, the height of the kite is approximately 10 feet.
Similar Questions
A kite is flying 98 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 59°. Find the length of the string. Round your answer to the nearest tenth.
Dmitri has let out 40 m of his kite string, which makes an angle of 72° with the horizontal ground. Show complete working for all answers. a. Find the height of the kite, to the nearest metre.b. Suppose the Sun is shining directly above the kite. How far is the kite’s shadow from Dmitri, to the nearest metre?
A pole 10 m high was observed from the point B where its shadow was equal to the pole Find the length of its shadow from another point on the same line where the angle of elevation of the top of the pole is 2/3 of the previous angle of elevation. step by step
Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28degrees ∘ . If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
A vertical stick 10m long casts a shadow 5m long on the ground. At the same time , a tower casts the shadow 30m long on the ground. Find the height of the tower ?Options100 m60 m80 m104 m
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.