Question

Use the triangle shown to find the ratios.

COS(A)= ?

tan(C) = ?

Answer 1

Explanation:

cos A=10/26=5/13

tan C=10/24=5/12

Answer 2

`\boxed {\boxed {\sf cos(A)= (5)/(13) \ and \ tan(C)= (5)/(12) }}`

Explanation:

The right triangle trigonometric ratios are:

• sin(θ)=opposite/hypotenuse
• cos(θ)=adjacent/hypotenuse
• tan(θ)= opposite/adjacent

We are asked to find the cosine of A. Therefore, we need the adjacent and hypotenuse.

• The hypotenuse of the triangle is 26, because it is opposite the right angle.
• The adjacent is 10, because it is next to angle A.

Substitute the values into the ratio.

• cos(θ)= adjacent/hypotenuse
• cos(A)= 10/26

Reduce the fraction. Both the numerator and denominator can be divided by 2.

• cos(A)= (10/2) / (26/2) = 5/13

We are also asked to find the tangent of C. We need the opposite and adjacent.

• The opposite is 10, because it is across from angle C.
• The adjacent is 24, because it is next to angle C.

Substitute the values into the ratio.

• tan(θ)= opposite/adjacent
• tan(C)= 10/24

Reduce the fraction. The numerator and denominator can be divided by 2.

• tan(C)= (10/2) / (24/2) = 5/12

The cosine of A is 5/13 and the tangent of C is 5/12