4b. What is the perimeter of ΔABC rounded to the nearest hundredth?

Question

In ΔABC, there is an altitude named BD. The length of AB is 10 units, the length of AC is 24 units. and m<A = 38°.

Answer 1

We need to get all the value of each side to get the perimeter and there is only one more side you need to find out then you add all the measures fo the sides:

You can use the Law of Cosine:

a² = b² + c² - 2bc• cos(m∠A)

Where:

a = BC

b = AC

c = AB

Given:

b = AC = 24

c = AB = 10

m∠A = 38˚

a² = 24² + 10² - 2•24•10• cos(38˚)

a² ≈ 297.75

a = BC ≈ 17.26

The perimeter is:

P =AB +BC + AC

P = 10 + 17.26 + 24 ≈ 51.26 units



*Make sure you round off only on the final answer.