A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a
short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
1 answer:
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The triangle is drawn and is shown in the image attached with.
We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.
D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:
AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units
So,
Therefore, the length of DE will be 3 units
We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.
D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:
AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units
So,
Therefore, the length of DE will be 3 units