Question

Point H is the point of intersection of the altitudes in acute triangle ABC. Given (CH = AB), find (mangle ACB), in degrees.

a) (30ᶜirc)

b) (45ᶜirc)

c) (60ᶜirc)

d) (90ᶜirc)

Answer 1

To find m∠ACB, let's assume CH = AB = x and use the Pythagorean theorem to find the length of AC. The altitudes in a triangle meet at a single point called the orthocenter, so m∠ACB = 90°.

Step-by-step explanation:

To find m∠ACB, we need to use the given information that CH = AB.

Let's assume that CH = AB = x.

Since CH is an altitude, it is perpendicular to AB. Therefore, triangle CHA is a right triangle.

Using the Pythagorean theorem, we can find the length of AC:

1. 
   
2. AC2 = CH2 + AH2
3. 
   
4. AC2 = x2 + x2 (since AH = HB)
5. 
   
6. AC2 = 2x2
7. 
   
8. AC = √(2x2)
9. 
   
10. AC = √2x

Then, to find m∠ACB, we use the fact that altitudes in a triangle meet at a single point called the orthocenter. So, m∠ACB = 90°.