△ABC is congruent to △DEF. What is the value of x? Explain how you determined your answer.
1 answer:
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Answer:
28.7 meters
Step-by-step explanation:
Draw a diagram. Let's say d is the distance between the anchor and the bottom of the tower, h is the height of the tower, and x is the length of the wire.
Using trigonometry, we can write two equations for the height of the tower:
h = d tan 65°
h = (d + 25) tan 35°
Setting these equal, we can solve for d.
d tan 65° = (d + 25) tan 35°
d tan 65° = d tan 35° + 25 tan 35°
d (tan 65° − tan 35°) = 25 tan 35°
d = 25 tan 35° / (tan 65° − tan 35°)
d ≈ 12.12
Now we can find x:
cos 65° = d / x
x = d / cos 65°
x ≈ 28.7
The wire is approximately 28.7 meters long.
