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Nikitich [7]
2 years ago
9

Given right triangle ABC with altitude BD is drawn to hypotenuse AC. If AB=5 and AD=1, what is the length of AC ? (Note: the fig

ure is not drawn to scale.)

Mathematics
1 answer:
Alex17521 [72]2 years ago
8 0

Answer:

x = 24.99 or 25

Step-by-step explanation:

<em>Using sin to figure out the angle of ABD, we can figure out the angle of CBD by subtracting it from 90°.</em>

sin y = (1/5)

y = 11.54°

90 - 11.54 = 78.46°

<em>Now using Pythagorean Theorem (</em><em>a²+b²=c²</em><em>) we can solve for line BD.</em>

1² + b² = 5²

1 + b² = 25

b² = 24

b = √24

<em>Now we can use tan to figure out the length of segment DC.</em>

tan(78.46) = z/√24

z = 23.99

<em>We can now combine the known length of segment AD and the length of DC to get </em><em>x</em><em>.</em>

1 + 23.99 = 24.99 or <u>about</u> 25.

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