Question

NO LINKS!!! Please help me with this trig problem. Use the diagram. Part 2

4. b= 4
c= 6
Find a, A, and B​

Answer 1

Answers:

• a = 2*sqrt(5) = 4.4721
• A = 48.1897 degrees
• B = 41.8103 degrees

The decimal values are approximate.

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Given info:

• b = 4
• c = 6

This is a right triangle, so we can use the pythagorean theorem to find the missing side 'a'.

a^2 + b^2 = c^2

a^2 + 4^2 = 6^2

a^2 + 16 = 36

a^2 = 36 - 16

a^2 = 20

a = sqrt(20)

a = sqrt(4*5)

a = sqrt(4)*sqrt(5)

a = 2*sqrt(5)

a = 4.4721 approximately

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To find the missing acute angles, we'll need a trig ratio.

There are many options to choose from. I'll use cosine to find angle A

cos(angle) = adjacent/hypotenuse

cos(A) = b/c

cos(A) = 4/6

cos(A) = 2/3

A = arccos(2/3) .... this is the same as
`\cos^(-1)`

A = 48.1897

For angle B, I'll use sine

sin(angle) = opposite/adjacent

sin(B) = b/c

sin(B) = 2/3

B = arcsin(2/3) .... same as
`\sin^(-1)`

B = 41.8103

Or you could use the fact that A+B = 90.

If you know A = 48.1897, then B = 90-A = 90-48.1897 = 41.8103

All of these decimal values are approximate.