Question

In △ABD, altitude AC⎯⎯⎯⎯⎯ intersects the right angle of ​ triangle ABD ​ at vertex A. BC=4.2 in. and CD=9.6 in.. What is the length of AC⎯⎯⎯⎯⎯?

Answer 1

To find the altitude AC in triangle ABD with sides BC and CD provided, apply the Pythagorean theorem. After calculating, we get AC ≈ 10.48 inches.

Step-by-step explanation:

The student has asked about finding the length of altitude AC in triangle ABD, given BC=4.2 in. and CD=9.6 in. The altitude in a right triangle is the segment perpendicular to the hypotenuse that divides the original right triangle into two smaller right triangles. In this scenario, the two smaller triangles ABC and ACD are similar to the larger triangle ABD.

Since we know the lengths of the segments BC and CD, we can use the Pythagorean theorem to determine the length of AC. As per the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, AC² = BC² + CD².

Calculating using the given measures, we find:

1. 
   
3. AC² = (4.2 in.)² + (9.6 in.)²
4. 
   
6. AC² = 17.64 in.² + 92.16 in.²
7. 
   
9. AC² = 109.8 in.²
10. 
    
12. AC = √109.8 in.²
13. 
    
15. AC ≈ 10.48 in.

Therefore, the length of the altitude AC is approximately 10.48 inches.