Question

In triangle ABC, the measure of angle B is 90 degrees, and BD is an altitude of the triangle. The length of AB is 15, and the length of AC is 23 greater than the length of AB. What is the value of BC/BD?

A) 8/3
B) 17/8
C)25/8
D)10/3

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Answer 1

To find the value of BC/BD in triangle ABC, we first need to find the length of AC. Then we can use the Pythagorean Theorem to find the length of BC. Finally, we can calculate BC/BD by dividing BC by BD.

Step-by-step explanation:

To find the value of BC/BD, we first need to find the length of AC. Given that AC is 23 greater than AB, we can set up an equation: AC = AB + 23. Since AB = 15, we can substitute it into the equation to find AC = 15 + 23 = 38.

Now, we can use the Pythagorean Theorem to find the length of BC. In a right triangle, the square of the hypotenuse (BC) is equal to the sum of the squares of the other two sides (AB and AC).

So we have BC^2 = AB^2 + AC^2 = 15^2 + 38^2 = 225 + 1444 = 1669. Taking the square root of both sides, we get BC = sqrt(1669).

Finally, we can calculate BC/BD by dividing BC by BD. Since BD is the altitude of the triangle, it is perpendicular to AC and forms a right triangle with BC. Therefore, BC/BD is equal to BC divided by the length of BD. Substituting the values, we have BC/BD = sqrt(1669) / 38.