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

Question

3 years ago

9

ure is not drawn to scale.)

1 answer:

Alex17521 [72] · Answer 1 · 2022-09-26T23:17:27+03:00

Answer:

x = 24.99 or 25

Step-by-step explanation:

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

sin y = (1/5)

y = 11.54°

90 - 11.54 = 78.46°

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

1² + b² = 5²

1 + b² = 25

b² = 24

b = √24

Now we can use tan to figure out the length of segment DC.

tan(78.46) = z/√24

z = 23.99

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

1 + 23.99 = 24.99 or about 25.