Question

Let AB = 24, AC = 10 and BC = 26.

a) What is the length of the leg opposite to ∠C?

b) What is the length of the leg adjacent to ∠C?

c) What is sin C?

d) What is cos C?

e) What is tan C?

Answer 1

a) 24

b) 10

c) 12/13

d) 5/13

e) 12/5

Explanation:

a) We can see that the leg opposite <C is AB, and we are given AB = 24

b) We can see the leg adjacent to <C is AC, and we are given that AC = 10

c) The trig function sine is equal to

`(opposite)/(hypotenuse)`

The opposite, AB, is 24, and the hypotenuse, BC, is 26. We can plug those numbers in:

`sin(c) = (24)/(26) = (12)/(13)`

d)The trig function cosine is equal to

`(adjacent)/(hypotenuse)`

The adjacent, AC, is 10, and the hypotenuse, BC, is 26. We can plug those numbers in:

`cos(c) = (10)/(26) = (5)/(13)`

d)The trig function tangent is equal to

`(opposite)/(adjacent)`

The opposite, AB, is 24, and the adjacent, AC, is 10. We can plug those numbers in:

`tan(c) = (24)/(10) = (12)/(5)`